Danielyan, S.; Guterman, A.; Kreines, E.; Pakovich, F. Integrability of matrices. (English) Zbl 07792525 Linear Algebra Appl. 684, 37-62 (2024). MSC: 15A20 15A21 15A18 12D05 26B05 26B12 26B15 PDFBibTeX XMLCite \textit{S. Danielyan} et al., Linear Algebra Appl. 684, 37--62 (2024; Zbl 07792525) Full Text: DOI arXiv
Monga, Z. B.; Shah, W. M. Bound estimates of the eigenvalues of matrix polynomials. (English) Zbl 07822492 J. Anal. 31, No. 4, 2973-2983 (2023). MSC: 12D10 30C15 15A18 15A42 65F15 PDFBibTeX XMLCite \textit{Z. B. Monga} and \textit{W. M. Shah}, J. Anal. 31, No. 4, 2973--2983 (2023; Zbl 07822492) Full Text: DOI
Monga, Z. B.; Shah, W. M. On zeros of matrix-valued analytic functions. (English) Zbl 07812128 Oper. Matrices 17, No. 2, 383-391 (2023). MSC: 12D10 15A18 30C15 PDFBibTeX XMLCite \textit{Z. B. Monga} and \textit{W. M. Shah}, Oper. Matrices 17, No. 2, 383--391 (2023; Zbl 07812128) Full Text: DOI
Duan, Cunxiang; van Dam, Edwin R.; Wang, Ligong The characteristic polynomials of uniform double hyperstars and uniform hypertriangles. (English) Zbl 1525.05092 Linear Algebra Appl. 678, 16-32 (2023). MSC: 05C31 05C65 05C50 12D05 15A18 PDFBibTeX XMLCite \textit{C. Duan} et al., Linear Algebra Appl. 678, 16--32 (2023; Zbl 1525.05092) Full Text: DOI
Shah, Wali Mohammad; Monga, Zahid Bashir On the bounds of the eigenvalues of matrix polynomials. (English) Zbl 07739511 Korean J. Math. 31, No. 2, 145-152 (2023). MSC: 15A42 15A18 12D10 30C10 PDFBibTeX XMLCite \textit{W. M. Shah} and \textit{Z. B. Monga}, Korean J. Math. 31, No. 2, 145--152 (2023; Zbl 07739511) Full Text: DOI
Nica, Bogdan; Sprague, Dacota Non-Archimedean views on Gershgorin’s theorem and diagonal dominance. (English) Zbl 1526.15010 Am. Math. Mon. 130, No. 3, 267-275 (2023). MSC: 15A18 15A42 12J25 26E30 PDFBibTeX XMLCite \textit{B. Nica} and \textit{D. Sprague}, Am. Math. Mon. 130, No. 3, 267--275 (2023; Zbl 1526.15010) Full Text: DOI
B, Pallavi.; Hadimani, Shrinath; Jayaraman, Sachindranath The Hoffman-Wielandt (type) inequality for quaternion matrices and quaternion matrix polynomials. arXiv:2302.07638 Preprint, arXiv:2302.07638 [math.SP] (2023). MSC: 15B33 15A42 15A18 15A20 12E15 15A66 BibTeX Cite \textit{Pallavi. B} et al., ``The Hoffman-Wielandt (type) inequality for quaternion matrices and quaternion matrix polynomials'', Preprint, arXiv:2302.07638 [math.SP] (2023) Full Text: arXiv OA License
Magalhães, Luis T. Simple proof of existence of a complex eigenvalue of a complex square matrix \(\ldots\)and yet another proof of the fundamental theorem of algebra with linear algebra. (English) Zbl 1508.15007 Linear Multilinear Algebra 70, No. 20, 5329-5333 (2022). Reviewer: Tin Yau Tam (Reno) MSC: 15A18 12D05 PDFBibTeX XMLCite \textit{L. T. Magalhães}, Linear Multilinear Algebra 70, No. 20, 5329--5333 (2022; Zbl 1508.15007) Full Text: DOI
de Seguins Pazzis, Clément The sum of two quadratic matrices: exceptional cases. (English) Zbl 1500.15024 Linear Algebra Appl. 653, 357-394 (2022). Reviewer: John D. Dixon (Ottawa) MSC: 15B33 15A21 15A18 11R32 12E10 PDFBibTeX XMLCite \textit{C. de Seguins Pazzis}, Linear Algebra Appl. 653, 357--394 (2022; Zbl 1500.15024) Full Text: DOI
Kalinina, Elizaveta A.; Smol’kin, Yurii A.; Uteshev, Alexei Yu. Stability and distance to instability for polynomial matrix families. Complex perturbations. (English) Zbl 1493.15053 Linear Multilinear Algebra 70, No. 7, 1291-1314 (2022). Reviewer: Olga M. Katkova (Boston) MSC: 15A22 15A18 15A15 18B05 12D10 30C15 47A55 PDFBibTeX XMLCite \textit{E. A. Kalinina} et al., Linear Multilinear Algebra 70, No. 7, 1291--1314 (2022; Zbl 1493.15053) Full Text: DOI
Berhuy, Grégory Minimal and characteristic polynomials of symmetric matrices in characteristic two. (English) Zbl 1495.15008 J. Algebra 593, 525-549 (2022). MSC: 15A18 15B33 15A63 12D99 PDFBibTeX XMLCite \textit{G. Berhuy}, J. Algebra 593, 525--549 (2022; Zbl 1495.15008) Full Text: DOI arXiv
Lei, Xiaoqiang \({}^{\alpha}_{\beta} \Omega\)-inclusion sets for general C-eigenvalues of a general piezoelectric-type tensor. (English) Zbl 1478.15037 Linear Multilinear Algebra 69, No. 16, 3043-3068 (2021). MSC: 15A69 15A18 65F15 65H17 12E10 PDFBibTeX XMLCite \textit{X. Lei}, Linear Multilinear Algebra 69, No. 16, 3043--3068 (2021; Zbl 1478.15037) Full Text: DOI
Hariprasad, M.; Venkatapathi, Murugesan Semi-analytical solutions for eigenvalue problems of chains and periodic graphs. (English) Zbl 1510.15020 Appl. Math. Comput. 411, Article ID 126512, 18 p. (2021). MSC: 15A18 65H04 12D10 15B05 26C10 PDFBibTeX XMLCite \textit{M. Hariprasad} and \textit{M. Venkatapathi}, Appl. Math. Comput. 411, Article ID 126512, 18 p. (2021; Zbl 1510.15020) Full Text: DOI arXiv
Bosch, Siegfried Linear algebra. A basic course with exercises trainer. 6th revised edition. (Lineare algebra. Ein Grundkurs mit Aufgabentrainer.) (English) Zbl 1457.15001 Berlin: Springer Spektrum (ISBN 978-3-662-62615-3/pbk; 978-3-662-62616-0/ebook). x, 503 p. (2021). MSC: 15-01 15B57 65F05 15A04 15A03 15A15 12D10 15A18 15A21 15A63 PDFBibTeX XMLCite \textit{S. Bosch}, Lineare algebra. Ein Grundkurs mit Aufgabentrainer. 6th revised edition. Berlin: Springer Spektrum (2021; Zbl 1457.15001) Full Text: DOI
Kaddoura, Issam; Mourad, Bassam On a class of matrices generated by certain generalized permutation matrices and applications. (English) Zbl 1425.15038 Linear Multilinear Algebra 67, No. 10, 2117-2134 (2019). MSC: 15B99 15A18 15A29 12D10 11C20 PDFBibTeX XMLCite \textit{I. Kaddoura} and \textit{B. Mourad}, Linear Multilinear Algebra 67, No. 10, 2117--2134 (2019; Zbl 1425.15038) Full Text: DOI
Ali, Istkhar; Truhar, Ninoslav Location of right eigenvalues of quaternionic matrix polynomials. (English) Zbl 1423.15009 Adv. Appl. Clifford Algebr. 29, No. 4, Paper No. 80, 21 p. (2019). Reviewer: Tin Yau Tam (Reno) MSC: 15A18 15A60 12E15 PDFBibTeX XMLCite \textit{I. Ali} and \textit{N. Truhar}, Adv. Appl. Clifford Algebr. 29, No. 4, Paper No. 80, 21 p. (2019; Zbl 1423.15009) Full Text: DOI
Melman, Aaron Cauchy, Gershgorin, and matrix polynomials. (English) Zbl 1407.15013 Math. Mag. 91, No. 4, 274-285 (2018). MSC: 15A18 12D10 30C15 PDFBibTeX XMLCite \textit{A. Melman}, Math. Mag. 91, No. 4, 274--285 (2018; Zbl 1407.15013) Full Text: DOI
Maccioni, Mauro The number of real eigenvectors of a real polynomial. (English) Zbl 1395.15009 Boll. Unione Mat. Ital. 11, No. 2, 125-145 (2018). MSC: 15A18 12D05 12D10 PDFBibTeX XMLCite \textit{M. Maccioni}, Boll. Unione Mat. Ital. 11, No. 2, 125--145 (2018; Zbl 1395.15009) Full Text: DOI arXiv
Melman, A. An alternative proof of Pellet’s theorem for matrix polynomials. (English) Zbl 1386.15026 Linear Multilinear Algebra 66, No. 4, 785-791 (2018). MSC: 15A18 12D10 30C10 30C15 PDFBibTeX XMLCite \textit{A. Melman}, Linear Multilinear Algebra 66, No. 4, 785--791 (2018; Zbl 1386.15026) Full Text: DOI
Dolcetti, Alberto; Pertici, Donato Some remarks on the Jordan-Chevalley decomposition. (English) Zbl 1386.15028 São Paulo J. Math. Sci. 11, No. 2, 385-404 (2017). MSC: 15A21 15A18 12J10 12J15 PDFBibTeX XMLCite \textit{A. Dolcetti} and \textit{D. Pertici}, São Paulo J. Math. Sci. 11, No. 2, 385--404 (2017; Zbl 1386.15028) Full Text: DOI arXiv
Tyaglov, Mikhail Self-interlacing polynomials. II: Matrices with self-interlacing spectrum. (English) Zbl 1375.15019 Electron. J. Linear Algebra 32, 51-57 (2017). MSC: 15A18 15B05 12D10 15B35 15B48 PDFBibTeX XMLCite \textit{M. Tyaglov}, Electron. J. Linear Algebra 32, 51--57 (2017; Zbl 1375.15019) Full Text: DOI arXiv
Ahmad, Sk. Safique; Ali, Istkhar Bounds for eigenvalues of matrix polynomials over quaternion division algebra. (English) Zbl 1405.15038 Adv. Appl. Clifford Algebr. 26, No. 4, 1095-1125 (2016). MSC: 15B33 12E15 15A42 34L15 15A18 15A66 PDFBibTeX XMLCite \textit{Sk. S. Ahmad} and \textit{I. Ali}, Adv. Appl. Clifford Algebr. 26, No. 4, 1095--1125 (2016; Zbl 1405.15038) Full Text: DOI
Dravie, Brandon; Parriaux, Jérémy; Guillot, Philippe; Millérioux, Gilles Matrix representations of vectorial Boolean functions and eigenanalysis. (English) Zbl 1372.94424 Cryptogr. Commun. 8, No. 4, 555-577 (2016). MSC: 94A60 06E30 12E20 15A18 15B34 PDFBibTeX XMLCite \textit{B. Dravie} et al., Cryptogr. Commun. 8, No. 4, 555--577 (2016; Zbl 1372.94424) Full Text: DOI HAL
Melman, A. Cauchy-like and Pellet-like results for polynomials. (English) Zbl 1342.12003 Linear Algebra Appl. 505, 174-193 (2016). MSC: 12D10 15A18 30C15 PDFBibTeX XMLCite \textit{A. Melman}, Linear Algebra Appl. 505, 174--193 (2016; Zbl 1342.12003) Full Text: DOI arXiv
Akian, Marianne; Bapat, Ravindra; Gaubert, Stéphane Non-archimedean valuations of eigenvalues of matrix polynomials. (English) Zbl 1341.15005 Linear Algebra Appl. 498, 592-627 (2016). MSC: 15A18 15A80 65F35 47A55 05C50 12K10 PDFBibTeX XMLCite \textit{M. Akian} et al., Linear Algebra Appl. 498, 592--627 (2016; Zbl 1341.15005) Full Text: DOI arXiv
Barone, M.; Lima, J. B.; Campello de Souza, R. M. The eigenstructure and Jordan form of the Fourier transform over fields of characteristic 2 and a generalized Vandermonde-type formula. (English) Zbl 1331.12004 Linear Algebra Appl. 494, 245-262 (2016). MSC: 12E20 15A18 15B33 43A32 PDFBibTeX XMLCite \textit{M. Barone} et al., Linear Algebra Appl. 494, 245--262 (2016; Zbl 1331.12004) Full Text: DOI
Li, Chaoqian; Jiao, Aiquan; Li, Yaotang An \(S\)-type eigenvalue localization set for tensors. (English) Zbl 1329.15029 Linear Algebra Appl. 493, 469-483 (2016). MSC: 15A18 15A69 12E10 PDFBibTeX XMLCite \textit{C. Li} et al., Linear Algebra Appl. 493, 469--483 (2016; Zbl 1329.15029) Full Text: DOI arXiv
Qin, Xuefeng; Zhong, Yulin; Huo, Yuanji Some anzahl theorems in singular orthogonal geometry over finite fields of odd characteristic. (Chinese. English summary) Zbl 1349.12001 Math. Pract. Theory 45, No. 5, 296-301 (2015). MSC: 12E20 15B10 15B33 15A18 PDFBibTeX XMLCite \textit{X. Qin} et al., Math. Pract. Theory 45, No. 5, 296--301 (2015; Zbl 1349.12001)
Melman, A. Nonscalar matrix polynomial representation of some scalar polynomials. (English) Zbl 1360.12001 Linear Algebra Appl. 474, 141-157 (2015). MSC: 12D10 15A18 30C10 30C15 PDFBibTeX XMLCite \textit{A. Melman}, Linear Algebra Appl. 474, 141--157 (2015; Zbl 1360.12001) Full Text: DOI
Benek Gursoy, Buket; Kirkland, Steve; Mason, Oliver; Sergeev, Sergeĭ The Markov chain tree theorem in commutative semirings and the state reduction algorithm in commutative semifields. (English) Zbl 1307.15053 Linear Algebra Appl. 468, 184-196 (2015). MSC: 15B51 16Y60 12K10 15A80 60J10 05C85 15A18 PDFBibTeX XMLCite \textit{B. Benek Gursoy} et al., Linear Algebra Appl. 468, 184--196 (2015; Zbl 1307.15053) Full Text: DOI arXiv
Batselier, Kim; Dreesen, Philippe; De Moor, Bart On the null spaces of the Macaulay matrix. (English) Zbl 1297.15041 Linear Algebra Appl. 460, 259-289 (2014). MSC: 15B99 13D02 16E05 15A18 12E05 PDFBibTeX XMLCite \textit{K. Batselier} et al., Linear Algebra Appl. 460, 259--289 (2014; Zbl 1297.15041) Full Text: DOI
Bosch, Siegfried Linear algebra. 5th revised ed. (Lineare Algebra.) (German) Zbl 1294.15001 Springer-Lehrbuch. Heidelberg: Springer Spektrum (ISBN 978-3-642-55259-5/pbk; 978-3-642-55260-1/ebook). x, 385 p. (2014). MSC: 15-01 15B57 65F05 15A04 15A03 15A15 12D10 15A18 15A21 15A63 PDFBibTeX XMLCite \textit{S. Bosch}, Lineare Algebra. 5th revised ed. Heidelberg: Springer Spektrum (2014; Zbl 1294.15001) Full Text: DOI
Melman, A. Inclusion disks for polynomial zeros in generalized bases. (English) Zbl 1302.12003 Linear Algebra Appl. 445, 326-346 (2014). MSC: 12D10 15A18 PDFBibTeX XMLCite \textit{A. Melman}, Linear Algebra Appl. 445, 326--346 (2014; Zbl 1302.12003) Full Text: DOI
Melman, A. Generalization and variations of Pellet’s theorem for matrix polynomials. (English) Zbl 1305.15029 Linear Algebra Appl. 439, No. 5, 1550-1567 (2013). MSC: 15A18 12D10 30C15 PDFBibTeX XMLCite \textit{A. Melman}, Linear Algebra Appl. 439, No. 5, 1550--1567 (2013; Zbl 1305.15029) Full Text: DOI arXiv
Melman, Aaron The twin of a theorem by Cauchy. (English) Zbl 1295.12001 Am. Math. Mon. 120, No. 2, 164-168 (2013). MSC: 12D10 15A18 30C15 PDFBibTeX XMLCite \textit{A. Melman}, Am. Math. Mon. 120, No. 2, 164--168 (2013; Zbl 1295.12001) Full Text: DOI
Melman, A. A single oval of Cassini for the zeros of a polynomial. (English) Zbl 1266.15030 Linear Multilinear Algebra 61, No. 2, 183-195 (2013). Reviewer: C. M. da Fonseca (Coimbra) MSC: 15A42 15A18 12D10 PDFBibTeX XMLCite \textit{A. Melman}, Linear Multilinear Algebra 61, No. 2, 183--195 (2013; Zbl 1266.15030) Full Text: DOI
Ma, Chao; Zhan, Xingzhi Extremal sparsity of the companion matrix of a polynomial. (English) Zbl 1269.15007 Linear Algebra Appl. 438, No. 1, 621-625 (2013). Reviewer: Cyril Fischer (Praha) MSC: 15A18 15A23 11C20 12E05 05C05 05C50 65F50 PDFBibTeX XMLCite \textit{C. Ma} and \textit{X. Zhan}, Linear Algebra Appl. 438, No. 1, 621--625 (2013; Zbl 1269.15007) Full Text: DOI
Chapman, Adam General polynomials over division algebras and left eigenvalues. (English) Zbl 1273.16028 Electron. J. Linear Algebra 23, 508-513 (2012). MSC: 16S36 16K20 11R52 15B33 15A18 12E15 PDFBibTeX XMLCite \textit{A. Chapman}, Electron. J. Linear Algebra 23, 508--513 (2012; Zbl 1273.16028) Full Text: DOI arXiv Link
Gupta, Sanjai; Rockstroh, Parousia; Su, Francis Edward Splitting fields and periods of Fibonacci sequences modulo primes. (English) Zbl 1246.15012 Math. Mag. 85, No. 2, 130-135 (2012). MSC: 15A18 12F10 97H60 97H40 PDFBibTeX XMLCite \textit{S. Gupta} et al., Math. Mag. 85, No. 2, 130--135 (2012; Zbl 1246.15012) Full Text: DOI arXiv Link
Melman, Aaron Modified Gershgorin disks for companion matrices. (English) Zbl 1253.15029 SIAM Rev. 54, No. 2, 355-373 (2012). Reviewer: Ludwig Elsner (Bielefeld) MSC: 15A42 15A18 12D10 65H04 PDFBibTeX XMLCite \textit{A. Melman}, SIAM Rev. 54, No. 2, 355--373 (2012; Zbl 1253.15029) Full Text: DOI
Cafuta, Kristijan; Klep, Igor; Povh, Janez Optimization and approximation of NC polynomials with sums of squares. (English) Zbl 1244.13002 Croat. Oper. Res. Rev. (CRORR) 1, 40-51 (2010). MSC: 13-04 14-04 12-04 90C90 14P10 90C22 15A18 PDFBibTeX XMLCite \textit{K. Cafuta} et al., Croat. Oper. Res. Rev. (CRORR) 1, 40--51 (2010; Zbl 1244.13002)
Butkovič, Peter Max-linear systems. Theory and algorithms. (English) Zbl 1202.15032 Springer Monographs in Mathematics. London: Springer (ISBN 978-1-84996-298-8/hbk; 978-1-4471-2583-9/pbk; 978-1-84996-299-5/ebook). xvii, 272 p. (2010). Reviewer: Constantin Popa (Constanţa) MSC: 15A80 15-02 90C27 15A18 15A06 15A39 12D05 15A03 16Y60 65F15 90C05 PDFBibTeX XMLCite \textit{P. Butkovič}, Max-linear systems. Theory and algorithms. London: Springer (2010; Zbl 1202.15032) Full Text: DOI
Machado, Armando Complex eigenvalues before the fundamental theorem of algebra. (English) Zbl 1223.15014 Linear Multilinear Algebra 57, No. 6, 561-566 (2009). Reviewer: Martin Plešinger (Liberec) MSC: 15A18 12D05 PDFBibTeX XMLCite \textit{A. Machado}, Linear Multilinear Algebra 57, No. 6, 561--566 (2009; Zbl 1223.15014) Full Text: DOI
Lecumberri, Pablo; Gómez, Marisol; Carlosena, Alfonso Generalized eigenvalues of nonsquare pencils with structure. (English) Zbl 1158.15005 SIAM J. Matrix Anal. Appl. 30, No. 1, 41-55 (2008). MSC: 15A18 15A22 65F15 12D05 PDFBibTeX XMLCite \textit{P. Lecumberri} et al., SIAM J. Matrix Anal. Appl. 30, No. 1, 41--55 (2008; Zbl 1158.15005) Full Text: DOI
Lam, T. Y.; Leroy, A.; Ozturk, A. Wedderburn polynomials over division rings. II. (English) Zbl 1173.16011 Jain, S.K. (ed.) et al., Noncommutative rings, group rings, diagram algebras and their applications. International conference, University of Madras, Chennai, India, December 18–22, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4285-0/pbk). Contemporary Mathematics 456, 73-98 (2008). Reviewer: Jean-Pierre E. Tignol (Louvain-La-Neuve) MSC: 16S36 16K40 15A18 16W22 12E10 PDFBibTeX XMLCite \textit{T. Y. Lam} et al., Contemp. Math. 456, 73--98 (2008; Zbl 1173.16011) Full Text: arXiv
Zeng, Guangxing A generalization of Stickelberger’s theorem. (English) Zbl 1140.15002 Linear Algebra Appl. 428, No. 11-12, 2880-2887 (2008). Reviewer: Salah Najib (Lille) MSC: 15A04 12Y05 15A18 13F20 13P10 14Q99 PDFBibTeX XMLCite \textit{G. Zeng}, Linear Algebra Appl. 428, No. 11--12, 2880--2887 (2008; Zbl 1140.15002) Full Text: DOI
Bosch, Siegfried Linear algebra. 4th revised ed. (Lineare Algebra.) (German) Zbl 1141.15300 Springer-Lehrbuch. Berlin: Springer (ISBN 978-3-540-76437-3/pbk). x, 297 p. (2008). MSC: 15-01 15B57 65F05 15A04 15A03 15A15 12D10 15A18 15A21 15A63 PDFBibTeX XMLCite \textit{S. Bosch}, Lineare Algebra. 4th revised ed. Berlin: Springer (2008; Zbl 1141.15300)
De Leo, Stefano; Ducati, Gisele; Leonardi, Vinicius Zeros of unilateral quaternionic polynomials. (English) Zbl 1151.15303 Electron. J. Linear Algebra 15, 297-313 (2006). MSC: 15B33 20G20 12Y05 65F15 15A18 PDFBibTeX XMLCite \textit{S. De Leo} et al., Electron. J. Linear Algebra 15, 297--313 (2006; Zbl 1151.15303) Full Text: DOI arXiv EuDML Link Link
Pan, V. Y.; Kunin, M.; Murphy, B.; Rosholt, R. E.; Tang, Y.; Yan, X.; Cao, W. Linking the TPR1, DPR1 and arrow-head matrix structures. (English) Zbl 1132.15009 Comput. Math. Appl. 52, No. 10-11, 1603-1608 (2006). MSC: 15A18 15B57 65H05 12Y05 26C10 65F15 PDFBibTeX XMLCite \textit{V. Y. Pan} et al., Comput. Math. Appl. 52, No. 10--11, 1603--1608 (2006; Zbl 1132.15009) Full Text: DOI
Bosch, Siegfried Linear algebra. 3rd ed. (Lineare Algebra.) (German) Zbl 1093.15500 Springer-Lehrbuch. Berlin: Springer (ISBN 3-540-29884-3). x, 295 p. (2006). MSC: 15-01 15B57 65F05 15A04 15A03 15A15 12D10 15A18 15A21 15A63 PDFBibTeX XMLCite \textit{S. Bosch}, Lineare Algebra. 3rd ed. Berlin: Springer (2006; Zbl 1093.15500) Full Text: DOI
Voevoda, A. A.; Chekhonadskikh, A. V. On the rank of the Jacobi matrix of the roots and coefficients of a polynomial. (Russian. English summary) Zbl 1104.12002 Pinus, A.G. (ed.) et al., Algebra and model theory 5. Collection of papers from the 5th summer school “Intermediate problems of model theory and universal algebra”, Erlogol, Russia, June 26–July 1, 2005. Novosibirsk: Novosibirsk State Technical University (ISBN 5-7782-0551-1/pbk). 275-280 (2005). MSC: 12E05 12Y05 13B05 15A18 PDFBibTeX XMLCite \textit{A. A. Voevoda} and \textit{A. V. Chekhonadskikh}, in: Algebra and model theory 5. Collection of papers from the 5th summer school ``Intermediate problems of model theory and universal algebra'', Erlogol, Russia, June 26--July 1, 2005. Novosibirsk: Novosibirsk State Technical University. 275--280 (2005; Zbl 1104.12002)
Derksen, Harm The fundamental theorem of algebra and linear algebra. (English) Zbl 1082.12002 Am. Math. Mon. 110, No. 7, 620-623 (2003). Reviewer: Alexander Shapiro (Rishon-le-Zion) MSC: 12D10 15A18 PDFBibTeX XMLCite \textit{H. Derksen}, Am. Math. Mon. 110, No. 7, 620--623 (2003; Zbl 1082.12002) Full Text: DOI
Niu, Xiao-Ming; Sakurai, Tetsuya A method for finding the zeros of polynomials using a companion matrix. (English) Zbl 1040.26005 Japan J. Ind. Appl. Math. 20, No. 2, 239-256 (2003). Reviewer: Michael M. Pahirya (Uzhgorod) MSC: 26C10 12D10 15A18 65H05 PDFBibTeX XMLCite \textit{X.-M. Niu} and \textit{T. Sakurai}, Japan J. Ind. Appl. Math. 20, No. 2, 239--256 (2003; Zbl 1040.26005) Full Text: DOI
Bosch, Siegfried Lineare Algebra. (Linear algebra). 2nd revised ed. (Lineare Algebra.) (German) Zbl 1016.15001 Springer-Lehrbuch. Berlin: Springer. x, 295 S. (2003). Reviewer: G.E.Wall (Sydney) MSC: 15-01 15B57 65F05 15A04 15A03 15A15 12D10 15A18 15A21 15A63 PDFBibTeX XMLCite \textit{S. Bosch}, Lineare Algebra. 2nd revised ed. Berlin: Springer (2003; Zbl 1016.15001)
Peretz, Ronen Iterations of concave maps, the Perron-Frobenius theory, and applications to circle packings. (English) Zbl 1022.05012 Electron. J. Linear Algebra 9, 197-254 (2002). Reviewer: Peter Boyvalenkov (Sofia) MSC: 05B40 52C15 11C20 15B48 15A60 47H07 15A18 15A42 35P15 47H10 52C25 12Y05 52C26 PDFBibTeX XMLCite \textit{R. Peretz}, Electron. J. Linear Algebra 9, 197--254 (2002; Zbl 1022.05012) Full Text: DOI EuDML EMIS
Kalman, Dan; White, James E. Polynomial equations and circulant matrices. (English) Zbl 1029.15021 Am. Math. Mon. 108, No. 9, 821-840 (2001). MSC: 15B57 12D10 26C10 30C15 15A18 11C08 PDFBibTeX XMLCite \textit{D. Kalman} and \textit{J. E. White}, Am. Math. Mon. 108, No. 9, 821--840 (2001; Zbl 1029.15021) Full Text: DOI
Bosch, Siegfried Linear algebra. (Lineare Algebra.) (German) Zbl 0988.15001 Springer-Lehrbuch. Berlin: Springer. x, 284 S. (2001). Reviewer: G.E.Wall (Sydney) MSC: 15-01 15A03 15A04 15A15 12D10 15A18 15A21 15A63 PDFBibTeX XMLCite \textit{S. Bosch}, Lineare Algebra. Berlin: Springer (2001; Zbl 0988.15001)
Bondyfalat, Didier; Mourrain, Bernard; Pan, Victor Y. Computation of a specified root of a polynomial system of equations using eigenvectors. (English) Zbl 0973.65038 Linear Algebra Appl. 319, No. 1-3, 193-209 (2000). Reviewer: B.Döring (Düsseldorf) MSC: 65H10 12Y05 15A18 12E12 PDFBibTeX XMLCite \textit{D. Bondyfalat} et al., Linear Algebra Appl. 319, No. 1--3, 193--209 (2000; Zbl 0973.65038) Full Text: DOI
Winkler, Joab R. A resultant matrix for scaled Bernstein polynomials. (English) Zbl 0970.12002 Linear Algebra Appl. 319, No. 1-3, 179-191 (2000). Reviewer: Edward J.Barbeau (Toronto) MSC: 12D05 12E05 11C08 15A18 PDFBibTeX XMLCite \textit{J. R. Winkler}, Linear Algebra Appl. 319, No. 1--3, 179--191 (2000; Zbl 0970.12002) Full Text: DOI
Uhlig, Frank General polynomial roots and their multiplicities in \(O(N)\) memory and \(O(N^2)\) time. (English) Zbl 1055.12504 Linear Multilinear Algebra 46, No. 4, 327-359 (1999). MSC: 12Y05 12D10 15A18 65F15 PDFBibTeX XMLCite \textit{F. Uhlig}, Linear Multilinear Algebra 46, No. 4, 327--359 (1999; Zbl 1055.12504) Full Text: DOI
Rupprecht, David An algorithm for computing certified approximate GCD of \(n\) univariate polynomials. (English) Zbl 0964.12007 J. Pure Appl. Algebra 139, No. 1-3, 255-284 (1999). Reviewer: V.Trevisan (Porto Alegre) MSC: 12Y05 65F30 15A18 65Y99 68W30 PDFBibTeX XMLCite \textit{D. Rupprecht}, J. Pure Appl. Algebra 139, No. 1--3, 255--284 (1999; Zbl 0964.12007) Full Text: DOI
Emiris, Ioannis Z.; Galligo, André; Lombardi, Henri Certified approximate univariate GCDs. (English) Zbl 0891.65015 J. Pure Appl. Algebra 117-118, 229-251 (1997). Reviewer: E.Minchev (Sofia) MSC: 65D20 12Y05 26C10 15A18 65Y20 68W30 PDFBibTeX XMLCite \textit{I. Z. Emiris} et al., J. Pure Appl. Algebra 117--118, 229--251 (1997; Zbl 0891.65015) Full Text: DOI
Williamson, Clifton J. On the algebraic construction of tri-diagonal matrices with given characteristic polynomial. (English) Zbl 0839.12002 Dilcher, Karl (ed.), Number theory. Fourth conference of the Canadian Number Theory Association, July 2-8, 1994, Dalhousie University, Halifax, Nova Scotia, Canada. Providence, RI: American Mathematical Society. CMS Conf. Proc. 15, 417-431 (1995). Reviewer: A.Kovačec (Coimbra) MSC: 12F10 15A18 12-04 13P10 PDFBibTeX XMLCite \textit{C. J. Williamson}, CMS Conf. Proc. 15, 417--431 (1995; Zbl 0839.12002)
Edelman, Alan; Kostlan, Eric The road from Kac’s matrix to Kac’s random polynomials. (English) Zbl 0817.15014 Lewis, John G. (ed.), Applied linear algebra. Proceedings of the 5th SIAM conference, held in Snowbird, UT, USA, June 15-18, 1994. Philadelphia, PA: SIAM. 503-507 (1994). Reviewer: H.-J.Kowalsky (Braunschweig) MSC: 15B57 15A18 12D10 60H25 42A05 PDFBibTeX XMLCite \textit{A. Edelman} and \textit{E. Kostlan}, in: Applied linear algebra. Proceedings of the 5th SIAM conference, held in Snowbird, UT, USA, June 15-18, 1994. Philadelphia, PA: SIAM. 503--507 (1994; Zbl 0817.15014)
Ifantis, E. K.; Panagopoulos, P. N. On the zeros of a class of polynomials defined by a three term recurrence relation. (English) Zbl 0801.12001 J. Math. Anal. Appl. 182, No. 2, 361-370 (1994). Reviewer: E.J.Barbeau (Toronto) MSC: 12D10 26C10 15A18 PDFBibTeX XMLCite \textit{E. K. Ifantis} and \textit{P. N. Panagopoulos}, J. Math. Anal. Appl. 182, No. 2, 361--370 (1994; Zbl 0801.12001) Full Text: DOI
Feng, Guochen; Wu, Wenda; Zhang, Shugong The eigenvalue problem equivalent to multivariate polynomial system. (English) Zbl 0842.15007 Numer. Math., J. Chin. Univ. 2, No. 2, 234-241 (1993). MSC: 15A18 15A22 12D10 PDFBibTeX XMLCite \textit{G. Feng} et al., Numer. Math., J. Chin. Univ. 2, No. 2, 234--241 (1993; Zbl 0842.15007)
Mornhinweg, David; Shapiro, Daniel B.; Valente, K. G. The principal axis theorem over arbitrary fields. (English) Zbl 0803.12001 Am. Math. Mon. 100, No. 8, 749-754 (1993). Reviewer: A.Sładek (Katowice) MSC: 12D15 12J15 15A21 15A18 PDFBibTeX XMLCite \textit{D. Mornhinweg} et al., Am. Math. Mon. 100, No. 8, 749--754 (1993; Zbl 0803.12001) Full Text: DOI
Feng, Guochen; Wu, Wenda; Huang, Kai Second equivalence theorem of multivariate polynomial system and eigenproblem. (English) Zbl 0921.15005 Adv. Math., Beijing 22, No. 5, 476-477 (1993). MSC: 15A18 12D05 PDFBibTeX XMLCite \textit{G. Feng} et al., Adv. Math., Beijing 22, No. 5, 476--477 (1993; Zbl 0921.15005)
Schmeisser, Gerhard A real symmetric tridiagonal matrix with a given characteristic polynomial. (English) Zbl 0793.15009 Linear Algebra Appl. 193, 11-18 (1993). Reviewer: R.Covaci (Cluj-Napoca) MSC: 15A21 15A18 12E10 PDFBibTeX XMLCite \textit{G. Schmeisser}, Linear Algebra Appl. 193, 11--18 (1993; Zbl 0793.15009) Full Text: DOI
Feng, Guochen; Wu, Wenda; Zhang, Shugong The eigenvalue problem equivalent to multivariate polynomial system. (English) Zbl 0797.15007 Northeast. Math. J. 9, No. 1, 5-8 (1993). Reviewer: J.Zemánek (Warszawa) MSC: 15A18 12D10 15A30 PDFBibTeX XMLCite \textit{G. Feng} et al., Northeast. Math. J. 9, No. 1, 5--8 (1993; Zbl 0797.15007)
Fiedler, Miroslav Expressing a polynomial as the characteristic polynomial of a symmetric matrix. (English) Zbl 0721.15005 Linear Algebra Appl. 141, 265-270 (1990). Reviewer: D.Ştefănescu (Bucureşti) MSC: 15A18 15B57 65H05 65F15 12D10 PDFBibTeX XMLCite \textit{M. Fiedler}, Linear Algebra Appl. 141, 265--270 (1990; Zbl 0721.15005) Full Text: DOI
Wood, D. W.; Turnbull, R. W.; Ball, J. K. Algebraic approximations to the locus of partition function zeros. (English) Zbl 0656.15019 J. Phys. A 20, 3495-3521 (1987). Reviewer: A.Actor MSC: 15A90 82B20 12D05 15A54 15A18 PDFBibTeX XMLCite \textit{D. W. Wood} et al., J. Phys. A, Math. Gen. 20, 3495--3521 (1987; Zbl 0656.15019) Full Text: DOI
Wood, D. W. The algebraic construction of partition function zeros: universality and algebraic cycles. (English) Zbl 0656.15018 J. Phys. A 20, 3471-3493 (1987). Reviewer: A.Actor MSC: 15A90 82B20 12D05 15A54 15A18 PDFBibTeX XMLCite \textit{D. W. Wood}, J. Phys. A, Math. Gen. 20, 3471--3493 (1987; Zbl 0656.15018) Full Text: DOI
Bulavskij, V. A.; Yakovleva, M. A. Generalized tridiagonal matrices and Sturm’s theorem. (English. Russian original) Zbl 0584.15003 Sov. Math., Dokl. 29, 185-188 (1984); translation from Dokl. Akad. Nauk SSSR 275, 277-280 (1984). Reviewer: M.Voicu MSC: 15A18 15A21 12D10 26C10 90C05 PDFBibTeX XMLCite \textit{V. A. Bulavskij} and \textit{M. A. Yakovleva}, Sov. Math., Dokl. 29, 185--188 (1984; Zbl 0584.15003); translation from Dokl. Akad. Nauk SSSR 275, 277--280 (1984)
Gutman, Shaul Matrix root clustering in algebraic regions. (English) Zbl 0529.93053 Int. J. Control 39, 773-778 (1984). MSC: 93D99 12D10 93B17 15A18 PDFBibTeX XMLCite \textit{S. Gutman}, Int. J. Control 39, 773--778 (1984; Zbl 0529.93053) Full Text: DOI
Cohn, P. M. Puiseux’s théorem revisited. (French) Zbl 0529.13011 J. Pure Appl. Algebra 31, 1-4 (1984). MSC: 13J05 13F25 15A18 12F05 PDFBibTeX XMLCite \textit{P. M. Cohn}, J. Pure Appl. Algebra 31, 1--4 (1984; Zbl 0529.13011) Full Text: DOI
Lancaster, P.; Tismenetsky, M. Some extensions and modifications of classical stability tests for polynomials. (English) Zbl 0526.93043 Int. J. Control 38, 369-380 (1983). MSC: 93D99 15A30 15A18 15B57 12D10 PDFBibTeX XMLCite \textit{P. Lancaster} and \textit{M. Tismenetsky}, Int. J. Control 38, 369--380 (1983; Zbl 0526.93043) Full Text: DOI
Hershkowitz, Daniel On the spectra of matrices having nonnegative sums of principal minors. (English) Zbl 0521.15004 Linear Algebra Appl. 55, 81-86 (1983). MSC: 15A18 15B48 12D10 PDFBibTeX XMLCite \textit{D. Hershkowitz}, Linear Algebra Appl. 55, 81--86 (1983; Zbl 0521.15004) Full Text: DOI
Sampson, J. H. Transformations linéaires et théorie de Galois. (French) Zbl 0517.12011 Gaz. Math., Soc. Math. Fr. 21, 85-88 (1983). Reviewer: N. Sankaran MSC: 12F10 15A04 15A18 PDFBibTeX XMLCite \textit{J. H. Sampson}, Gaz. Math., Soc. Math. Fr. 21, 85--88 (1983; Zbl 0517.12011)
Weiss, Alfred Characteristic polynomials of symmetric matrices. (English) Zbl 0504.12020 Ternary quadratic forms and norms, Semin. 1974/75, Lect. Notes Pure Appl. Math. 79, 59-74 (1982). MSC: 12E05 15B57 15A18 15B33 11S99 PDFBibTeX XML
Roppenecker, G.; Preuss, H.-P. Nullstellen und Pole linearer Mehrgroessensysteme. I: Grundlagen und Definitionen. (German) Zbl 0485.93044 Regelungstechnik 30, 219-225 (1982). MSC: 93C35 93B25 12D10 93B17 93C05 93C99 15A18 15A21 PDFBibTeX XMLCite \textit{G. Roppenecker} and \textit{H. P. Preuss}, Regelungstechnik 30, 219--225 (1982; Zbl 0485.93044)
Gohberg, Israel; Kaashoek, M. A.; Lerer, L.; Rodman, Leiba Common multiples and common divisors of matrix polynomials. I: Spectral method. (English) Zbl 0449.15015 Indiana Univ. Math. J. 30, 321-356 (1981). MSC: 15A54 15A18 15A23 12D05 PDFBibTeX XMLCite \textit{I. Gohberg} et al., Indiana Univ. Math. J. 30, 321--356 (1981; Zbl 0449.15015) Full Text: DOI
Beesack, Paul R. The spread of matrices and polynomials. (English) Zbl 0473.15009 Linear Algebra Appl. 31, 145-149 (1980). MSC: 15A42 15A18 12D10 PDFBibTeX XMLCite \textit{P. R. Beesack}, Linear Algebra Appl. 31, 145--149 (1980; Zbl 0473.15009) Full Text: DOI
Crilly, Tony Finite vector spaces from rotating triangles. (English) Zbl 0414.15001 Math. Mag. 52, 163-168 (1979). MSC: 15A03 15A18 51M20 12F05 PDFBibTeX XMLCite \textit{T. Crilly}, Math. Mag. 52, 163--168 (1979; Zbl 0414.15001) Full Text: DOI
Bahl, Christian A.; Cain, Bryan E. The inertia of diagonal multiples of \(3\times 3\) real matrices. (English) Zbl 0379.15004 Linear Algebra Appl. 18, 267-280 (1977). MSC: 15A18 12D10 PDFBibTeX XMLCite \textit{C. A. Bahl} and \textit{B. E. Cain}, Linear Algebra Appl. 18, 267--280 (1977; Zbl 0379.15004) Full Text: DOI
Chalkley, Roger Quartic equations and tetrahedral symmetries. (English) Zbl 0341.12101 Math. Mag. 48, 211-215 (1975). MSC: 12E10 51M20 15A18 PDFBibTeX XMLCite \textit{R. Chalkley}, Math. Mag. 48, 211--215 (1975; Zbl 0341.12101) Full Text: DOI
Friedland, Shmuel On inverse multiplicative eigenvalue problems for matrices. (English) Zbl 0329.15003 Linear Algebra Appl. 12, 127-137 (1975). MSC: 15A18 12D10 PDFBibTeX XMLCite \textit{S. Friedland}, Linear Algebra Appl. 12, 127--137 (1975; Zbl 0329.15003) Full Text: DOI
Jury, E. I.; Ahn, S. M. Remarks on the root-clustering of a polynomial in a certain region in the complex plane. (English) Zbl 0306.30006 Q. appl. Math. 32, 203-205 (1974). MSC: 30C15 15A18 12D10 PDFBibTeX XMLCite \textit{E. I. Jury} and \textit{S. M. Ahn}, Q. Appl. Math. 32, 203--205 (1974; Zbl 0306.30006) Full Text: DOI
Fiedler, M. On a theorem by A. Horn. (English) Zbl 0271.15006 Math. Struct., comput. Math., math. Modelling (to appear). MSC: 15B57 12J15 15A18 PDFBibTeX XML
Lehnigk, Siegfried H. On the Hermite matrix. (English) Zbl 0251.15010 Trans. sixteenth Conf. Army Math. 1970, U.S. Army Res. Office Durham Rep. No. 71-2, 377-387 (1971). MSC: 15A18 15B57 12D10 93C05 PDFBibTeX XML
Aitken, A. C. Further numerical studies in algebraic equations and matrices. (English) Zbl 0002.00703 Proc. R. Soc. Edinb. 51, 80-90 (1931). Reviewer: Karl Pingitzer (Wien) MSC: 12D10 15A18 65H05 PDFBibTeX XMLCite \textit{A. C. Aitken}, Proc. R. Soc. Edinburgh 51, 80--90 (1931; Zbl 0002.00703) Full Text: DOI
Scott, B. J. On some theorems in determinants. (English) JFM 10.0115.01 Messenger (2) VIII. 32-37 (1879). Reviewer: Glaisher, Prof. (Cambridge) (Ohrtmann, Dr. (Berlin)) MSC: 15A15 15A18 12D05 11R27 26A09 26B10 05A10 PDFBibTeX XML
Gravelaar, N. L. W. A. A peculiar parallel. (Eene byzondere vergelijking.) (Dutch) JFM 10.0116.01 Nieuw Arch. IV, 113-124 (1878). Reviewer: van Geer, Prof. (Leiden) MSC: 12E12 15A15 15A18 12D10 PDFBibTeX XMLCite \textit{N. L. W. A. Gravelaar}, Nieuw Arch. 4, 113--124 (1878; JFM 10.0116.01)
Minozzi, A. Upon a determinant. (Sopra un determinante.) (Italian) JFM 10.0113.02 Battaglini G. XVI, 148-151 (1878). Reviewer: Stolz, Prof. (Innsbruck) MSC: 15A15 12E12 15A18 12D05 11R27 33C65 15A06 33B10 26C10 PDFBibTeX XMLCite \textit{A. Minozzi}, Battaglini G. 16, 148--151 (1878; JFM 10.0113.02)
Mansion, P. On a pair of algebraical equations. (English) JFM 09.0102.02 Messenger (2) VII. 57-58 (1877). Reviewer: Glaisher, Prof. (Cambridge) (Ohrtmann, Dr. (Berlin)) MSC: 12E12 15A15 15A18 65H10 PDFBibTeX XML
Glaisher, J. W. L. On the factors of a special form of determinants. (English) JFM 10.0112.03 Quart. J. XV, 347-356 (1877). MSC: 15A15 12D05 11R27 15A18 05E05 PDFBibTeX XMLCite \textit{J. W. L. Glaisher}, Quart. J. 15, 347--356 (1877; JFM 10.0112.03)