Tian, Yongge Some new characterizations of a Hermitian matrix and their applications. (English) Zbl 07785402 Complex Anal. Oper. Theory 18, No. 1, Paper No. 2, 8 p. (2024). MSC: 15B57 15A09 15A24 PDFBibTeX XMLCite \textit{Y. Tian}, Complex Anal. Oper. Theory 18, No. 1, Paper No. 2, 8 p. (2024; Zbl 07785402) Full Text: DOI
Tian, Yongge On a family of matrix equalities that involve multiple products of generalized inverses. (English) Zbl 1518.15005 Aequationes Math. 97, No. 3, 563-574 (2023). Reviewer: Ilya Spitkovsky (Williamsburg) MSC: 15A09 15A24 PDFBibTeX XMLCite \textit{Y. Tian}, Aequationes Math. 97, No. 3, 563--574 (2023; Zbl 1518.15005) Full Text: DOI
Liu, Ming; Tian, Yongge; Yuan, Ruixia Statistical inference of a partitioned linear random-effects model. (English) Zbl 07649699 Commun. Stat., Theory Methods 52, No. 4, 1251-1272 (2023). MSC: 15A10 62H12 62J05 62J10 PDFBibTeX XMLCite \textit{M. Liu} et al., Commun. Stat., Theory Methods 52, No. 4, 1251--1272 (2023; Zbl 07649699) Full Text: DOI
Tian, Yongge Characterizations of the group invertibility of a matrix revisited. (English) Zbl 1504.15015 Demonstr. Math. 55, 866-890 (2022). MSC: 15A09 15A24 15A45 PDFBibTeX XMLCite \textit{Y. Tian}, Demonstr. Math. 55, 866--890 (2022; Zbl 1504.15015) Full Text: DOI
Tian, Yongge A study of range equalities for mixed products of two matrices and their generalized inverses. (English) Zbl 1513.15007 Comput. Appl. Math. 41, No. 8, Paper No. 384, 17 p. (2022). MSC: 15A09 15A10 PDFBibTeX XMLCite \textit{Y. Tian}, Comput. Appl. Math. 41, No. 8, Paper No. 384, 17 p. (2022; Zbl 1513.15007) Full Text: DOI
Tian, Yongge Equivalence analysis of different reverse order laws for generalized inverses of a matrix product. (English) Zbl 1501.15004 Indian J. Pure Appl. Math. 53, No. 4, 939-947 (2022). MSC: 15A09 15A24 PDFBibTeX XMLCite \textit{Y. Tian}, Indian J. Pure Appl. Math. 53, No. 4, 939--947 (2022; Zbl 1501.15004) Full Text: DOI
Jiang, Bo; Liu, Ming; Tian, Yongge On two correlated linear models with common and different parameters. (English) Zbl 1524.62256 Math. Slovaca 72, No. 5, 1355-1374 (2022). MSC: 62H12 62J05 15A10 62J10 PDFBibTeX XMLCite \textit{B. Jiang} et al., Math. Slovaca 72, No. 5, 1355--1374 (2022; Zbl 1524.62256) Full Text: DOI
Ma, Rong; Tian, Yongge A matrix approach to a general partitioned linear model with partial parameter restrictions. (English) Zbl 1498.15002 Linear Multilinear Algebra 70, No. 13, 2513-2532 (2022). MSC: 15A06 15B52 15A09 62H12 62J05 PDFBibTeX XMLCite \textit{R. Ma} and \textit{Y. Tian}, Linear Multilinear Algebra 70, No. 13, 2513--2532 (2022; Zbl 1498.15002) Full Text: DOI
Jiang, Bo; Tian, Yongge Invariance property of a five matrix product involving two generalized inverses. (English) Zbl 1524.15007 An. Științ. Univ. “Ovidius” Constanța, Ser. Mat. 29, No. 1, 83-92 (2021). MSC: 15A09 15A24 47A05 PDFBibTeX XMLCite \textit{B. Jiang} and \textit{Y. Tian}, An. Științ. Univ. ``Ovidius'' Constanța, Ser. Mat. 29, No. 1, 83--92 (2021; Zbl 1524.15007) Full Text: DOI
Tian, Yongge Miscellaneous reverse order laws and their equivalent facts for generalized inverses of a triple matrix product. (English) Zbl 1490.15006 AIMS Math. 6, No. 12, 13845-13886 (2021). MSC: 15A09 15A10 15A24 PDFBibTeX XMLCite \textit{Y. Tian}, AIMS Math. 6, No. 12, 13845--13886 (2021; Zbl 1490.15006) Full Text: DOI
Sun, Yuqin; Jiang, Hong; Tian, Yongge A prediction analysis in a constrained multivariate general linear model with future observations. (English) Zbl 07532125 Commun. Stat., Theory Methods 50, No. 2, 345-357 (2021). MSC: 15A09 62H12 62H25 62J05 62-XX PDFBibTeX XMLCite \textit{Y. Sun} et al., Commun. Stat., Theory Methods 50, No. 2, 345--357 (2021; Zbl 07532125) Full Text: DOI
Tian, Yongge Classification analysis to the equalities \(A^{(i,\dots,j)}=B^{(k,\dots,l)}\) for generalized inverses of two matrices. (English) Zbl 1473.15010 Linear Multilinear Algebra 69, No. 8, 1383-1406 (2021). MSC: 15A09 15A10 15A24 47A05 47A50 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Multilinear Algebra 69, No. 8, 1383--1406 (2021; Zbl 1473.15010) Full Text: DOI
Tian, Yongge; Wang, Jie Some remarks on fundamental formulas and facts in the statistical analysis of a constrained general linear model. (English) Zbl 1511.62159 Commun. Stat., Theory Methods 49, No. 5, 1201-1216 (2020). MSC: 62J05 15A09 62F30 62H12 62J20 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{J. Wang}, Commun. Stat., Theory Methods 49, No. 5, 1201--1216 (2020; Zbl 1511.62159) Full Text: DOI
Tian, Yongge Miscellaneous equalities for idempotent matrices with applications. (English) Zbl 1478.15003 Open Math. 18, 671-714 (2020). MSC: 15A03 15A09 15A27 47A05 PDFBibTeX XMLCite \textit{Y. Tian}, Open Math. 18, 671--714 (2020; Zbl 1478.15003) Full Text: DOI
Tian, Yongge Miscellaneous reverse order laws for generalized inverses of matrix products with applications. (English) Zbl 1446.15003 Adv. Oper. Theory 5, No. 4, 1889-1942 (2020). MSC: 15A09 15A10 15A24 47A05 PDFBibTeX XMLCite \textit{Y. Tian}, Adv. Oper. Theory 5, No. 4, 1889--1942 (2020; Zbl 1446.15003) Full Text: DOI
Tian, Yongge Two groups of mixed reverse order laws for generalized inverses of two and three matrix products. (English) Zbl 1449.15005 Comput. Appl. Math. 39, No. 3, Paper No. 181, 15 p. (2020). MSC: 15A09 15A24 47A05 PDFBibTeX XMLCite \textit{Y. Tian}, Comput. Appl. Math. 39, No. 3, Paper No. 181, 15 p. (2020; Zbl 1449.15005) Full Text: DOI
Tian, Yongge On relationships between two linear subspaces and two orthogonal projectors. (English) Zbl 1433.15005 Spec. Matrices 7, 142-212 (2019). MSC: 15A03 15A09 15A24 15A27 15B57 47A15 47H05 PDFBibTeX XMLCite \textit{Y. Tian}, Spec. Matrices 7, 142--212 (2019; Zbl 1433.15005) Full Text: DOI
Tian, Yongge Formulas for calculating the dimensions of the sums and the intersections of a family of linear subspaces with applications. (English) Zbl 1425.15001 Beitr. Algebra Geom. 60, No. 3, 471-485 (2019). Reviewer: Janko Marovt (Maribor) MSC: 15A03 15A09 PDFBibTeX XMLCite \textit{Y. Tian}, Beitr. Algebra Geom. 60, No. 3, 471--485 (2019; Zbl 1425.15001) Full Text: DOI
Jiang, Bo; Tian, Yongge Necessary and sufficient conditions for nonlinear matrix identities to always hold. (English) Zbl 1414.15022 Aequationes Math. 93, No. 3, 587-600 (2019). Reviewer: John D. Dixon (Ottawa) MSC: 15A24 15A09 16E50 47A50 PDFBibTeX XMLCite \textit{B. Jiang} and \textit{Y. Tian}, Aequationes Math. 93, No. 3, 587--600 (2019; Zbl 1414.15022) Full Text: DOI
Tian, Yongge; Jiang, Bo Closed-form formulas for calculating the max-min ranks of a triple matrix product composed by generalized inverses. (English) Zbl 1413.15002 Comput. Appl. Math. 37, No. 5, 5876-5919 (2018). MSC: 15A03 15A09 15A24 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{B. Jiang}, Comput. Appl. Math. 37, No. 5, 5876--5919 (2018; Zbl 1413.15002) Full Text: DOI
Tian, Yongge How to establish exact formulas for calculating the max-min ranks of products of two matrices and their generalized inverses. (English) Zbl 1386.15007 Linear Multilinear Algebra 66, No. 1, 22-73 (2018). MSC: 15A03 15A09 15A24 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Multilinear Algebra 66, No. 1, 22--73 (2018; Zbl 1386.15007) Full Text: DOI
Jiang, Bo; Tian, Yongge Rank/inertia approaches to weighted least-squares solutions of linear matrix equations. (English) Zbl 1426.15020 Appl. Math. Comput. 315, 400-413 (2017). MSC: 15A24 15A09 62H12 62J05 PDFBibTeX XMLCite \textit{B. Jiang} and \textit{Y. Tian}, Appl. Math. Comput. 315, 400--413 (2017; Zbl 1426.15020) Full Text: DOI
Tian, Yongge Upper and lower bounds for the rank of the matrix-valued function \(A+BXC\) when \(X\) has a fixed rank. (English) Zbl 1387.15013 Linear Multilinear Algebra 65, No. 10, 2101-2113 (2017). MSC: 15A23 15A24 65F05 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Multilinear Algebra 65, No. 10, 2101--2113 (2017; Zbl 1387.15013) Full Text: DOI
Tian, Yongge; Jiang, Bo Quadratic properties of least-squares solutions of linear matrix equations with statistical applications. (English) Zbl 1417.15018 Comput. Stat. 32, No. 4, 1645-1663 (2017). MSC: 15A24 15B57 62J05 62H12 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{B. Jiang}, Comput. Stat. 32, No. 4, 1645--1663 (2017; Zbl 1417.15018) Full Text: DOI
Jiang, Bo; Tian, Yongge; Zhang, Xuan On decompositions of estimators under a general linear model with partial parameter restrictions. (English) Zbl 06819962 Open Math. 15, 1300-1322 (2017). MSC: 62F10 62F30 15A03 15A09 PDFBibTeX XMLCite \textit{B. Jiang} et al., Open Math. 15, 1300--1322 (2017; Zbl 06819962) Full Text: DOI
Tian, Yongge Matrix rank and inertia formulas in the analysis of general linear models. (English) Zbl 1359.15003 Open Math. 15, 126-150 (2017). MSC: 15A03 15A09 62H12 62J05 PDFBibTeX XMLCite \textit{Y. Tian}, Open Math. 15, 126--150 (2017; Zbl 1359.15003) Full Text: DOI
Tian, Yongge; Guo, Wenxing On comparison of dispersion matrices of estimators under a constrained linear model. (English) Zbl 1392.62209 Stat. Methods Appl. 25, No. 4, 623-649 (2016). MSC: 62J05 15A09 62H12 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{W. Guo}, Stat. Methods Appl. 25, No. 4, 623--649 (2016; Zbl 1392.62209) Full Text: DOI
Tian, Yongge Solutions of a constrained Hermitian matrix-valued function optimization problem with applications. (English) Zbl 1357.65079 Oper. Matrices 10, No. 4, 967-983 (2016). Reviewer: Hang Lau (Montréal) MSC: 65K05 15A09 15A24 47A62 90C22 PDFBibTeX XMLCite \textit{Y. Tian}, Oper. Matrices 10, No. 4, 967--983 (2016; Zbl 1357.65079) Full Text: DOI
Tian, Yongge; Jiang, Bo An algebraic study of BLUPs under two linear random-effects models with correlated covariance matrices. (English) Zbl 1358.15012 Linear Multilinear Algebra 64, No. 12, 2351-2367 (2016). Reviewer: Chen Sheng (Harbin) MSC: 15A24 15A09 62H12 62J05 62J10 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{B. Jiang}, Linear Multilinear Algebra 64, No. 12, 2351--2367 (2016; Zbl 1358.15012) Full Text: DOI
Tian, Yongge Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications. (English) Zbl 1344.15003 J. Inequal. Appl. 2016, Paper No. 182, 51 p. (2016). MSC: 15A03 15A09 15A24 PDFBibTeX XMLCite \textit{Y. Tian}, J. Inequal. Appl. 2016, Paper No. 182, 51 p. (2016; Zbl 1344.15003) Full Text: DOI
Tian, Yongge; Jiang, Bo Matrix rank/inertia formulas for least-squares solutions with statistical applications. (English) Zbl 1333.15006 Spec. Matrices 4, 130-140 (2016). MSC: 15A24 62J05 15A16 15A03 15A18 62F30 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{B. Jiang}, Spec. Matrices 4, 130--140 (2016; Zbl 1333.15006) Full Text: DOI
Tian, Yongge; Guo, Wenxing Some equalities and inequalities for the Hermitian Moore-Penrose inverse of triple matrix product with applications. (English) Zbl 1340.15009 J. Math. Res. Appl. 35, No. 3, 321-329 (2015). MSC: 15A09 15A45 15B57 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{W. Guo}, J. Math. Res. Appl. 35, No. 3, 321--329 (2015; Zbl 1340.15009) Full Text: DOI
Tian, Yongge A matrix handling of predictions of new observations under a general random-effects model. (English) Zbl 1329.62321 Electron. J. Linear Algebra 29, 30-45 (2015). MSC: 62J05 15A09 62H12 PDFBibTeX XMLCite \textit{Y. Tian}, Electron. J. Linear Algebra 29, 30--45 (2015; Zbl 1329.62321) Full Text: DOI
Tian, Yongge A survey on rank and inertia optimization problems of the matrix-valued function \(A+BXB^\ast\). (English) Zbl 1327.15007 Numer. Algebra Control Optim. 5, No. 3, 289-326 (2015). MSC: 15A09 15A24 65K10 65K15 PDFBibTeX XMLCite \textit{Y. Tian}, Numer. Algebra Control Optim. 5, No. 3, 289--326 (2015; Zbl 1327.15007) Full Text: DOI
Tian, Yongge; Wang, Yufu Expansion formulas for orthogonal projectors onto ranges of row block matrices. (English) Zbl 1313.15004 J. Math. Res. Appl. 34, No. 2, 147-154 (2014). MSC: 15A03 15A09 15A27 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Wang}, J. Math. Res. Appl. 34, No. 2, 147--154 (2014; Zbl 1313.15004) Full Text: DOI
Li, Ying; Tian, Yongge On relations among solutions of the Hermitian matrix equation \(AXA^* = B\) and its three small equations. (English) Zbl 1296.15009 Ann. Funct. Anal. 5, No. 2, 30-46 (2014). MSC: 15A24 15B57 PDFBibTeX XMLCite \textit{Y. Li} and \textit{Y. Tian}, Ann. Funct. Anal. 5, No. 2, 30--46 (2014; Zbl 1296.15009) Full Text: DOI EMIS
Tian, Yongge How to solve three fundamental linear matrix inequalities in the Löwner partial ordering. (English) Zbl 1297.15024 J. Math. Inequal. 8, No. 1, 1-54 (2014). Reviewer: Fozi Dannan (Damascus) MSC: 15A45 15A24 15A09 15A39 15B57 PDFBibTeX XMLCite \textit{Y. Tian}, J. Math. Inequal. 8, No. 1, 1--54 (2014; Zbl 1297.15024) Full Text: DOI arXiv Link
Tian, Yongge Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions. (English) Zbl 1278.15019 Banach J. Math. Anal. 8, No. 1, 148-178 (2014). MSC: 15A24 15B57 15A03 90C11 90C22 15A18 PDFBibTeX XMLCite \textit{Y. Tian}, Banach J. Math. Anal. 8, No. 1, 148--178 (2014; Zbl 1278.15019) Full Text: DOI arXiv Euclid Link
Tian, Yongge Least-squares solutions and least-rank solutions of the matrix equation \(AXA^{*}=B\) and their relations. (English) Zbl 1313.65095 Numer. Linear Algebra Appl. 20, No. 5, 713-722 (2013). MSC: 65F30 15A24 65F20 PDFBibTeX XMLCite \textit{Y. Tian}, Numer. Linear Algebra Appl. 20, No. 5, 713--722 (2013; Zbl 1313.65095) Full Text: DOI
Tian, Yongge; Wang, Hongxing Relations between least-squares and least-rank solutions of the matrix equation \(AXB=C\). (English) Zbl 1293.15012 Appl. Math. Comput. 219, No. 20, 10293-10301 (2013). MSC: 15A24 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{H. Wang}, Appl. Math. Comput. 219, No. 20, 10293--10301 (2013; Zbl 1293.15012) Full Text: DOI
Liu, Yonghui; Tian, Yongge Hermitian-type generalized singular value decomposition with applications. (English) Zbl 1289.65108 Numer. Linear Algebra Appl. 20, No. 1, 60-73 (2013). Reviewer: Iveta Hnetynkova (Praha) MSC: 65F30 15A24 65F20 15B57 15A03 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{Y. Tian}, Numer. Linear Algebra Appl. 20, No. 1, 60--73 (2013; Zbl 1289.65108) Full Text: DOI
Tian, Yongge Biquaternions and their complex matrix representations. (English) Zbl 1280.15011 Beitr. Algebra Geom. 54, No. 2, 575-592 (2013). Reviewer: Dmitri Artamonov (Moscow) MSC: 15B33 15A06 15A24 15A23 15A18 15A15 15A60 PDFBibTeX XMLCite \textit{Y. Tian}, Beitr. Algebra Geom. 54, No. 2, 575--592 (2013; Zbl 1280.15011) Full Text: DOI
Tian, Yongge Solutions of the matrix inequalities in the minus partial ordering and Löwner partial ordering. (English) Zbl 1273.15002 Math. Inequal. Appl. 16, No. 3, 861-872 (2013). MSC: 15A03 15A09 15A24 15B57 PDFBibTeX XMLCite \textit{Y. Tian}, Math. Inequal. Appl. 16, No. 3, 861--872 (2013; Zbl 1273.15002) Full Text: DOI arXiv
Tian, Yongge Equalities and inequalities for Hermitian solutions and Hermitian definite solutions of the two matrix equations \(AX = B\) and \(AXA ^{*} = B\). (English) Zbl 1281.15016 Aequationes Math. 86, No. 1-2, 107-135 (2013). Reviewer: Mihail Voicu (Iaşi) MSC: 15A24 15A03 15A09 15B57 PDFBibTeX XMLCite \textit{Y. Tian}, Aequationes Math. 86, No. 1--2, 107--135 (2013; Zbl 1281.15016) Full Text: DOI arXiv
Tian, Yongge Analytical formulas for calculating the extremal ranks of the matrix-valued function \(A + BXC\) when the rank of \(X\) is fixed. arXiv:1301.3675 Preprint, arXiv:1301.3675 [math.OC] (2013). MSC: 15A03 15A23 15A24 65F05 BibTeX Cite \textit{Y. Tian}, ``Analytical formulas for calculating the extremal ranks of the matrix-valued function $A + BXC$ when the rank of $X$ is fixed'', Preprint, arXiv:1301.3675 [math.OC] (2013) Full Text: arXiv OA License
Tian, Yongge Closed-form formulas for calculating the extremal ranks and inertias of a quadratic matrix-valued function and their applications. arXiv:1301.2567 Preprint, arXiv:1301.2567 [math.OC] (2013). MSC: 15A24 15B57 65K10 90C20 90C22 BibTeX Cite \textit{Y. Tian}, ``Closed-form formulas for calculating the extremal ranks and inertias of a quadratic matrix-valued function and their applications'', Preprint, arXiv:1301.2567 [math.OC] (2013) Full Text: arXiv OA License
Tian, Yongge Analytical solutions to some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix inequalities. arXiv:1301.0986 Preprint, arXiv:1301.0986 [math.OC] (2013). MSC: 15A24 15A39 15A45 15B57 49K30 65K10 90C11 90C22 BibTeX Cite \textit{Y. Tian}, ``Analytical solutions to some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix inequalities'', Preprint, arXiv:1301.0986 [math.OC] (2013) Full Text: arXiv OA License
Tian, Yongge Solutions to 18 constrained optimization problems on the rank and inertia of the linear matrix function. (English) Zbl 1255.15010 Math. Comput. Modelling 55, No. 3-4, 955-968 (2012). MSC: 15A18 PDFBibTeX XMLCite \textit{Y. Tian}, Math. Comput. Modelling 55, No. 3--4, 955--968 (2012; Zbl 1255.15010) Full Text: DOI
Tian, Yongge; Li, Ying Distributions of eigenvalues and inertias of some block Hermitian matrices consisting of orthogonal projectors. (English) Zbl 1261.15013 Linear Multilinear Algebra 60, No. 9, 1027-1069 (2012). Reviewer: Alan L. Andrew (Bundoora) MSC: 15A18 15A03 15A42 15B57 65F15 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Li}, Linear Multilinear Algebra 60, No. 9, 1027--1069 (2012; Zbl 1261.15013) Full Text: DOI
Tian, Yongge Characterizing relationships between estimations under a general linear model with explicit and implicit restrictions by rank of matrix. (English) Zbl 1271.62152 Commun. Stat., Theory Methods 41, No. 13-14, 2588-2601 (2012). MSC: 62J05 62H12 62F30 15A99 PDFBibTeX XMLCite \textit{Y. Tian}, Commun. Stat., Theory Methods 41, No. 13--14, 2588--2601 (2012; Zbl 1271.62152) Full Text: DOI
Tian, Yongge; Von Rosen, Dietrich Solving the matrix inequality \(AXB + (AXB)^{*} \geqslant C\). (English) Zbl 1246.15008 Math. Inequal. Appl. 15, No. 3, 537-548 (2012). MSC: 15A09 15A24 15A39 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{D. Von Rosen}, Math. Inequal. Appl. 15, No. 3, 537--548 (2012; Zbl 1246.15008) Full Text: DOI
Tian, Yongge Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications. (English) Zbl 1252.15026 Linear Algebra Appl. 437, No. 3, 835-859 (2012). Reviewer: Süleyman Güler (Aydin) MSC: 15A54 15A24 15A63 15B57 90C20 90C22 15B48 15A18 65K05 15A45 15A03 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Algebra Appl. 437, No. 3, 835--859 (2012; Zbl 1252.15026) Full Text: DOI
Tian, Yongge On additive decomposition of the Hermitian solution of the matrix equation \(AXA^* = B\). (English) Zbl 1241.15012 Mediterr. J. Math. 9, No. 1, 47-60 (2012). Reviewer: Grozio Stanilov (Sofia) MSC: 15A24 15A03 15A09 15B57 PDFBibTeX XMLCite \textit{Y. Tian}, Mediterr. J. Math. 9, No. 1, 47--60 (2012; Zbl 1241.15012) Full Text: DOI
Tian, Yongge Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method. (English) Zbl 1236.65070 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 2, 717-734 (2012). Reviewer: Hans Benker (Merseburg) MSC: 65K05 15A09 15A24 15A63 15B10 15B57 PDFBibTeX XMLCite \textit{Y. Tian}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 2, 717--734 (2012; Zbl 1236.65070) Full Text: DOI
Liu, Yonghui; Tian, Yongge A simultaneous decomposition of a matrix triplet with applications. (English) Zbl 1249.15020 Numer. Linear Algebra Appl. 18, No. 1, 69-85 (2011). Reviewer: Iveta Hnětýnková (Praha) MSC: 15A24 15A23 15A03 15B57 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{Y. Tian}, Numer. Linear Algebra Appl. 18, No. 1, 69--85 (2011; Zbl 1249.15020) Full Text: DOI
Tian, Yongge; Zhang, Jieping Some equalities for estimations of partial coefficients under a general linear regression model. (English) Zbl 1229.62075 Stat. Pap. 52, No. 4, 911-920 (2011). MSC: 62H12 62J05 15A09 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{J. Zhang}, Stat. Pap. 52, No. 4, 911--920 (2011; Zbl 1229.62075) Full Text: DOI
Tian, Yongge A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications. (English) Zbl 1235.15007 Linear Multilinear Algebra 59, No. 11, 1237-1246 (2011). Reviewer: Kaiming Zhao (Waterloo) MSC: 15A09 15A24 15A27 15B57 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Multilinear Algebra 59, No. 11, 1237--1246 (2011; Zbl 1235.15007) Full Text: DOI
Tian, Yongge Solving a minus partial ordering equation over von Neumann regular rings. (English) Zbl 1230.16011 Rev. Mat. Complut. 24, No. 2, 335-342 (2011). MSC: 16E50 15A06 15A09 16D25 PDFBibTeX XMLCite \textit{Y. Tian}, Rev. Mat. Complut. 24, No. 2, 335--342 (2011; Zbl 1230.16011) Full Text: DOI
Tian, Yongge Relations between matrix sets generated from linear matrix expressions and their applications. (English) Zbl 1217.15021 Comput. Math. Appl. 61, No. 6, 1493-1501 (2011). MSC: 15A24 15A09 PDFBibTeX XMLCite \textit{Y. Tian}, Comput. Math. Appl. 61, No. 6, 1493--1501 (2011; Zbl 1217.15021) Full Text: DOI
Tian, Yongge Extremal ranks of a quadratic matrix expression with applications. (English) Zbl 1220.15006 Linear Multilinear Algebra 59, No. 6, 627-644 (2011). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15A03 15A09 15A24 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Multilinear Algebra 59, No. 6, 627--644 (2011; Zbl 1220.15006) Full Text: DOI
Liu, Yonghui; Tian, Yongge Max-min problems on the ranks and inertias of the matrix expressions \(A - BXC \pm (BXC)^{\ast}\) with applications. (English) Zbl 1223.90077 J. Optim. Theory Appl. 148, No. 3, 593-622 (2011). Reviewer: Zhang Xian (Xiamen) MSC: 90C47 15A09 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{Y. Tian}, J. Optim. Theory Appl. 148, No. 3, 593--622 (2011; Zbl 1223.90077) Full Text: DOI
Tian, Yongge Maximization and minimization of the rank and inertia of the Hermitian matrix expression \(A-BX-(BX)^{*}\) with applications. (English) Zbl 1211.15022 Linear Algebra Appl. 434, No. 10, 2109-2139 (2011). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15A24 15A03 15A42 15B57 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Algebra Appl. 434, No. 10, 2109--2139 (2011; Zbl 1211.15022) Full Text: DOI
Tian, Yongge Two universal similarity factorization equalities for commutative involutory and idempotent matrices and their applications. (English) Zbl 1256.15007 Linear Multilinear Algebra 59, No. 1-3, 129-144 (2011). Reviewer: Witold Więsław (Wrocław) MSC: 15A23 15A27 15A15 15A09 15A03 15A21 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Multilinear Algebra 59, No. 1--3, 129--144 (2011; Zbl 1256.15007) Full Text: DOI
Tian, Yongge Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors. (English) Zbl 1217.15015 J. Math. Anal. Appl. 376, No. 1, 162-186 (2011). Reviewer: Jaspal Singh Aujla (Jalandhar) MSC: 15A18 15A22 15B57 PDFBibTeX XMLCite \textit{Y. Tian}, J. Math. Anal. Appl. 376, No. 1, 162--186 (2011; Zbl 1217.15015) Full Text: DOI
Tian, Yongge; Wang, Hongxing Characterizations of EP matrices and weighted-EP matrices. (English) Zbl 1209.15039 Linear Algebra Appl. 434, No. 5, 1295-1318 (2011). Reviewer: Václav Burjan (Praha) MSC: 15B57 15A09 15A03 15A24 15A27 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{H. Wang}, Linear Algebra Appl. 434, No. 5, 1295--1318 (2011; Zbl 1209.15039) Full Text: DOI
Tian, Yongge Weighted least-squares estimators of parametric functions of the regression coefficients under a general linear model. (English) Zbl 1432.62214 Ann. Inst. Stat. Math. 62, No. 5, 929-941 (2010). MSC: 62J05 15B48 62H12 PDFBibTeX XMLCite \textit{Y. Tian}, Ann. Inst. Stat. Math. 62, No. 5, 929--941 (2010; Zbl 1432.62214) Full Text: DOI
Tian, Yongge; Tian, Zhe On additive and block decompositions of WLSEs under a multiple partitioned regression model. (English) Zbl 1283.62146 Statistics 44, No. 4, 361-379 (2010). MSC: 62J05 62H12 15A09 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Z. Tian}, Statistics 44, No. 4, 361--379 (2010; Zbl 1283.62146) Full Text: DOI
Tian, Yongge Equalities for orthogonal projectors and their operations. (English) Zbl 1223.15010 Cent. Eur. J. Math. 8, No. 5, 855-870 (2010). Reviewer: Qing-Wen Wang (Shanghai) MSC: 15A09 15A03 15A27 15B10 15B57 PDFBibTeX XMLCite \textit{Y. Tian}, Cent. Eur. J. Math. 8, No. 5, 855--870 (2010; Zbl 1223.15010) Full Text: DOI
Tian, Yongge Completing block Hermitian matrices with maximal and minimal ranks and inertias. (English) Zbl 1207.15029 Electron. J. Linear Algebra 21, 124-141 (2010). MSC: 15A83 15A03 15B57 15A18 15A23 PDFBibTeX XMLCite \textit{Y. Tian}, Electron. J. Linear Algebra 21, 124--141 (2010; Zbl 1207.15029) Full Text: DOI EuDML EMIS
Tian, Yongge Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix. (English) Zbl 1207.15007 Electron. J. Linear Algebra 20, 226-240 (2010). MSC: 15A09 15B57 15A03 15A23 15A18 PDFBibTeX XMLCite \textit{Y. Tian}, Electron. J. Linear Algebra 20, 226--240 (2010; Zbl 1207.15007) Full Text: EuDML EMIS
Tian, Yongge On additive decompositions of solutions of the matrix equation \(AXB=C\). (English) Zbl 1214.15009 Calcolo 47, No. 4, 193-209 (2010). Reviewer: Vladimir P. Kostov (Nice) MSC: 15A24 15A03 15A09 PDFBibTeX XMLCite \textit{Y. Tian}, Calcolo 47, No. 4, 193--209 (2010; Zbl 1214.15009) Full Text: DOI
Tian, Yongge Solving some linear equations over alternative rings. (English) Zbl 1201.17019 Result. Math. 58, No. 3-4, 355-364 (2010). Reviewer: K. C. Sivakumar (Chennai) MSC: 17D05 15A09 17A30 PDFBibTeX XMLCite \textit{Y. Tian}, Result. Math. 58, No. 3--4, 355--364 (2010; Zbl 1201.17019) Full Text: DOI
Tian, Yong Ge Estimations of parametric functions under a system of linear regression equations with correlated errors. (English) Zbl 1197.62062 Acta Math. Sin., Engl. Ser. 26, No. 10, 1927-1942 (2010). MSC: 62H12 62J05 15A09 PDFBibTeX XMLCite \textit{Y. G. Tian}, Acta Math. Sin., Engl. Ser. 26, No. 10, 1927--1942 (2010; Zbl 1197.62062) Full Text: DOI
Tian, Yongge On equalities of estimations of parametric functions under a general linear model and its restricted models. (English) Zbl 1197.62020 Metrika 72, No. 3, 313-330 (2010). MSC: 62F10 62J05 15A09 62F30 PDFBibTeX XMLCite \textit{Y. Tian}, Metrika 72, No. 3, 313--330 (2010; Zbl 1197.62020) Full Text: DOI
Liu, Yonghui; Tian, Yongge How to use RSVD to solve the matrix equation \(A=BXC\). (English) Zbl 1202.15019 Linear Multilinear Algebra 58, No. 5-6, 537-543 (2010). Reviewer: Constantin Popa (Constanţa) MSC: 15A24 15A03 15A23 15A22 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{Y. Tian}, Linear Multilinear Algebra 58, No. 5--6, 537--543 (2010; Zbl 1202.15019) Full Text: DOI
Tian, Yongge; Liu, Chunmei Some equalities for estimations of variance components in a general linear model and its restricted and transformed models. (English) Zbl 1203.62107 J. Multivariate Anal. 101, No. 9, 1959-1969 (2010). MSC: 62H12 62J05 62J10 15A09 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{C. Liu}, J. Multivariate Anal. 101, No. 9, 1959--1969 (2010; Zbl 1203.62107) Full Text: DOI
Tian, Yongge Equalities and inequalities for inertias of Hermitian matrices with applications. (English) Zbl 1205.15033 Linear Algebra Appl. 433, No. 1, 263-296 (2010). Reviewer: Edgar Pereira (Covilha) MSC: 15A42 15A24 15A45 15B57 15A03 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Algebra Appl. 433, No. 1, 263--296 (2010; Zbl 1205.15033) Full Text: DOI
Tian, Yongge Solving two pairs of quadratic equations in quaternions. (English) Zbl 1188.15015 Adv. Appl. Clifford Algebr. 20, No. 1, 185-193 (2010). MSC: 15A24 15B33 PDFBibTeX XMLCite \textit{Y. Tian}, Adv. Appl. Clifford Algebr. 20, No. 1, 185--193 (2010; Zbl 1188.15015) Full Text: DOI
Liu, Yonghui; Tian, Yongge Extremal ranks of submatrices in an Hermitian solution to the matrix equation \(AXA^{*}=B\) with applications. (English) Zbl 1194.15014 J. Appl. Math. Comput. 32, No. 2, 289-301 (2010). Reviewer: Sheng Chen (Harbin) MSC: 15A24 15A09 15A03 15B57 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{Y. Tian}, J. Appl. Math. Comput. 32, No. 2, 289--301 (2010; Zbl 1194.15014) Full Text: DOI
Tian, Yongge Eight expressions for generalized inverses of a bordered matrix. (English) Zbl 1188.15006 Linear Multilinear Algebra 58, No. 1-2, 203-220 (2010). Reviewer: Sheng Chen (Harbin) MSC: 15A09 15A03 PDFBibTeX XMLCite \textit{Y. Tian}, Linear Multilinear Algebra 58, No. 1--2, 203--220 (2010; Zbl 1188.15006) Full Text: DOI
Tian, Yongge; Takane, Yoshio The inverse of any two-by-two nonsingular partitioned matrix and three matrix inverse completion problems. (English) Zbl 1186.15005 Comput. Math. Appl. 57, No. 8, 1294-1304 (2009). MSC: 15A09 15A83 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Takane}, Comput. Math. Appl. 57, No. 8, 1294--1304 (2009; Zbl 1186.15005) Full Text: DOI
Liu, Yonghui; Tian, Yongge A mixed-type reverse order law for generalized inverse of a triple matrix product. (Chinese. English summary) Zbl 1199.15021 Acta Math. Sin., Chin. Ser. 52, No. 1, 197-204 (2009). MSC: 15A09 15A24 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{Y. Tian}, Acta Math. Sin., Chin. Ser. 52, No. 1, 197--204 (2009; Zbl 1199.15021)
Liu, Yonghui; Tian, Yongge; Takane, Yoshio Ranks of Hermitian and skew-Hermitian solutions to the matrix equation \(AXA^*=B\). (English) Zbl 1180.15018 Linear Algebra Appl. 431, No. 12, 2359-2372 (2009). Reviewer: Václav Burjan (Praha) MSC: 15A24 15A09 15A03 15B57 PDFBibTeX XMLCite \textit{Y. Liu} et al., Linear Algebra Appl. 431, No. 12, 2359--2372 (2009; Zbl 1180.15018) Full Text: DOI
Tian, Yongge; Takane, Yoshio On \(\mathbf V\)-orthogonal projectors associated with a semi-norm. (English) Zbl 1332.15016 Ann. Inst. Stat. Math. 61, No. 2, 517-530 (2009). MSC: 15A09 15A03 62H12 62J05 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Takane}, Ann. Inst. Stat. Math. 61, No. 2, 517--530 (2009; Zbl 1332.15016) Full Text: DOI
Tian, Yongge Some properties of submatrices in a solution to the matrix equation \(AXB=C\) with applications. (English) Zbl 1168.15307 J. Franklin Inst. 346, No. 6, 557-569 (2009). MSC: 15A24 15A03 15A09 PDFBibTeX XMLCite \textit{Y. Tian}, J. Franklin Inst. 346, No. 6, 557--569 (2009; Zbl 1168.15307) Full Text: DOI
Tian, Yongge; Styan, George P. H. On some matrix equalities for generalized inverses with applications. (English) Zbl 1165.15006 Linear Algebra Appl. 430, No. 10, 2716-2733 (2009). Reviewer: Mohammad Sal Moslehian (Mashhad) MSC: 15A09 15A24 15A03 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{G. P. H. Styan}, Linear Algebra Appl. 430, No. 10, 2716--2733 (2009; Zbl 1165.15006) Full Text: DOI
Tian, Yongge; Puntanen, Simo On the equivalence of estimations under a general linear model and its transformed models. (English) Zbl 1160.62330 Linear Algebra Appl. 430, No. 10, 2622-2641 (2009). MSC: 62H12 62J05 62F30 15A09 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{S. Puntanen}, Linear Algebra Appl. 430, No. 10, 2622--2641 (2009; Zbl 1160.62330) Full Text: DOI
Tian, Yongge Approximation and continuity of Moore-Penrose inverses of orthogonal row block matrices. (English) Zbl 1163.15004 Appl. Math. Comput. 210, No. 1, 18-25 (2009). Reviewer: Mohammad Sal Moslehian (Mashhad) MSC: 15A09 15A24 15A45 15A60 PDFBibTeX XMLCite \textit{Y. Tian}, Appl. Math. Comput. 210, No. 1, 18--25 (2009; Zbl 1163.15004) Full Text: DOI
Tian, Yongge; Takane, Yoshio More on generalized inverses of partitioned matrices with Banachiewicz-Schur forms. (English) Zbl 1162.15002 Linear Algebra Appl. 430, No. 5-6, 1641-1655 (2009). Reviewer: Sheng Chen (Harbin) MSC: 15A09 15A03 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Takane}, Linear Algebra Appl. 430, No. 5--6, 1641--1655 (2009; Zbl 1162.15002) Full Text: DOI
Liu, Yonghui; Tian, Yongge More on extremal ranks of the matrix expressions \(A-BX \pm X^{*}B^{*}\) with statistical applications. (English) Zbl 1212.15029 Numer. Linear Algebra Appl. 15, No. 4, 307-325 (2008). MSC: 15A24 65F30 15A22 62J05 65F20 62F10 15A03 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{Y. Tian}, Numer. Linear Algebra Appl. 15, No. 4, 307--325 (2008; Zbl 1212.15029) Full Text: DOI
Tian, Yongge; Takane, Yoshio Some properties of projectors associated with the WLSE under a general linear model. (English) Zbl 1141.62043 J. Multivariate Anal. 99, No. 6, 1070-1082 (2008). MSC: 62H12 62J05 15A09 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Takane}, J. Multivariate Anal. 99, No. 6, 1070--1082 (2008; Zbl 1141.62043) Full Text: DOI
Tian, Yongge; Takane, Yoshio Some algebraic and statistical properties of {WLSE}s under a general growth curve model. (English) Zbl 1152.62349 Electron. J. Linear Algebra 16, 187-203 (2007). MSC: 62H12 15A09 15A03 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Takane}, Electron. J. Linear Algebra 16, 187--203 (2007; Zbl 1152.62349) Full Text: EuDML
Tian, Yongge; Liu, Yonghui On a group of mixed-type reverse-order laws for generalized inverses of a triple matrix product with applications. (English) Zbl 1141.15008 Electron. J. Linear Algebra 16, 73-89 (2007). Reviewer: Jinhai Chen (Hongkong) MSC: 15A09 15A03 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Liu}, Electron. J. Linear Algebra 16, 73--89 (2007; Zbl 1141.15008) Full Text: EuDML
Tian, Yongge Some mixed-type reverse-order laws for the Moore-Penrose inverse of a triple matrix product. (English) Zbl 1152.15007 Rocky Mt. J. Math. 37, No. 4, 1327-1347 (2007). Reviewer: Nestor Thome (Valencia) MSC: 15A09 15A03 PDFBibTeX XMLCite \textit{Y. Tian}, Rocky Mt. J. Math. 37, No. 4, 1327--1347 (2007; Zbl 1152.15007) Full Text: DOI Euclid
Takane, Yoshio; Tian, Yongge; Yanai, Haruo On constrained generalized inverses of matrices and their properties. (English) Zbl 1133.62339 Ann. Inst. Stat. Math. 59, No. 4, 807-820 (2007). MSC: 62J05 15A09 62H12 PDFBibTeX XMLCite \textit{Y. Takane} et al., Ann. Inst. Stat. Math. 59, No. 4, 807--820 (2007; Zbl 1133.62339) Full Text: DOI
Takane, Yoshio; Tian, Yongge; Yanai, Haruo On reverse-order laws for least-squares g-inverses and minimum norm g-inverses of a matrix product. (English) Zbl 1125.15006 Aequationes Math. 73, No. 1-2, 56-70 (2007). Reviewer: Nestor Thome (Valencia) MSC: 15A09 15A03 PDFBibTeX XMLCite \textit{Y. Takane} et al., Aequationes Math. 73, No. 1--2, 56--70 (2007; Zbl 1125.15006) Full Text: DOI
Tian, Yongge; Liu, Yonghui Extremal ranks of some symmetric matrix expressions with applications. (English) Zbl 1123.15001 SIAM J. Matrix Anal. Appl. 28, No. 3, 890-905 (2006). Reviewer: Václav Burjan (Praha) MSC: 15A03 15A09 15A24 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Liu}, SIAM J. Matrix Anal. Appl. 28, No. 3, 890--905 (2006; Zbl 1123.15001) Full Text: DOI
Liu, Yonghui; Tian, Yongee The extremal ranks of \(A_1-B_1XC_1\) subject to a pair of matrix equations. (English) Zbl 1167.15300 Rend. Semin. Mat. Univ. Padova 116, 55-69 (2006). MSC: 15A03 15A24 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{Y. Tian}, Rend. Semin. Mat. Univ. Padova 116, 55--69 (2006; Zbl 1167.15300) Full Text: EuDML
Tian, Yongge; Takane, Yoshio On common generalized inverses of a pair of matrices. (English) Zbl 1116.15009 Linear Multilinear Algebra 54, No. 3, 195-209 (2006). Reviewer: Nestor Thome (Valencia) MSC: 15A09 15A03 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Takane}, Linear Multilinear Algebra 54, No. 3, 195--209 (2006; Zbl 1116.15009) Full Text: DOI
Tian, Yongge Universal similarity factorization equalities over generalized Clifford algebras. (English) Zbl 1106.15022 Acta Math. Sin., Engl. Ser. 22, No. 1, 289-300 (2006). Reviewer: Georgi Hristov Georgiev (Shumen) MSC: 15A66 15B33 15A23 15A18 PDFBibTeX XMLCite \textit{Y. Tian}, Acta Math. Sin., Engl. Ser. 22, No. 1, 289--300 (2006; Zbl 1106.15022) Full Text: DOI