Allred, Sarah; Curl, Emelie; Fallat, Shaun; Nasserasr, Shahla; Schuerger, Houston; Villagrán, Ralihe R.; Vishwakarma, Prateek K. The strong spectral property of graphs: graph operations and barbell partitions. (English) Zbl 07805289 Graphs Comb. 40, No. 2, Paper No. 20, 25 p. (2024). MSC: 05C50 05C76 15A18 15A29 PDFBibTeX XMLCite \textit{S. Allred} et al., Graphs Comb. 40, No. 2, Paper No. 20, 25 p. (2024; Zbl 07805289) Full Text: DOI arXiv
Deaett, Louis; Fallat, Shaun; Furst, Veronika; Hutchens, John; Mitchell, Lon; Zhang, Yaqi Sparks of symmetric matrices and their graphs. (English) Zbl 07807938 Electron. J. Linear Algebra 39, 591-606 (2023). MSC: 05C50 15A18 15A29 PDFBibTeX XMLCite \textit{L. Deaett} et al., Electron. J. Linear Algebra 39, 591--606 (2023; Zbl 07807938) Full Text: DOI
Barrett, Wayne; Fallat, Shaun; Furst, Veronika; Nasserasr, Shahla; Rooney, Brendan; Tait, Michael Regular graphs of degree at most four that allow two distinct eigenvalues. (English) Zbl 1526.05087 Linear Algebra Appl. 679, 127-164 (2023). MSC: 05C50 05C07 15A29 15A18 PDFBibTeX XMLCite \textit{W. Barrett} et al., Linear Algebra Appl. 679, 127--164 (2023; Zbl 1526.05087) Full Text: DOI arXiv
Abiad, Aida; Fallat, Shaun M.; Kempton, Mark; Levene, Rupert H.; Oblak, Polona; Šmigoc, Helena; Tait, Michael; Vander Meulen, Kevin N. Bordering of symmetric matrices and an application to the minimum number of distinct eigenvalues for the join of graphs. (English) Zbl 1526.05085 Linear Algebra Appl. 679, 104-126 (2023). MSC: 05C50 15A18 05C76 PDFBibTeX XMLCite \textit{A. Abiad} et al., Linear Algebra Appl. 679, 104--126 (2023; Zbl 1526.05085) Full Text: DOI arXiv
Barrett, Wayne; Fallat, Shaun; Furst, Veronika; Kenter, Franklin; Nasserasr, Shahla; Rooney, Brendan; Tait, Michael; van der Holst, Hein Sparsity of graphs that allow two distinct eigenvalues. (English) Zbl 1518.05111 Linear Algebra Appl. 674, 377-395 (2023). MSC: 05C50 05C42 15A29 15A18 PDFBibTeX XMLCite \textit{W. Barrett} et al., Linear Algebra Appl. 674, 377--395 (2023; Zbl 1518.05111) Full Text: DOI arXiv
Deaett, Louis; Fallat, Shaun; Furst, Veronika; Hutchens, John; Mitchell, Lon; Zhang, Yaqi The Spark of Symmetric Matrices Described by a Graph. arXiv:2307.00376 Preprint, arXiv:2307.00376 [math.CO] (2023). MSC: 05C50 15A18 15A29 BibTeX Cite \textit{L. Deaett} et al., ``The Spark of Symmetric Matrices Described by a Graph'', Preprint, arXiv:2307.00376 [math.CO] (2023) Full Text: arXiv OA License
Li, Honghai; Su, Li; Fallat, Shaun On a relationship between the characteristic and matching polynomials of a uniform hypertree. arXiv:2306.16247 Preprint, arXiv:2306.16247 [math.CO] (2023). MSC: 15A18 05C65 05C50 BibTeX Cite \textit{H. Li} et al., ``On a relationship between the characteristic and matching polynomials of a uniform hypertree'', Preprint, arXiv:2306.16247 [math.CO] (2023) Full Text: arXiv OA License
Fallat, Shaun M.; Vishwakarma, Prateek Kumar Inequalities for totally nonnegative matrices: Gantmacher–Krein, Karlin, and Laplace. arXiv:2305.16485 Preprint, arXiv:2305.16485 [math.CA] (2023). MSC: 05C50 15A15 15B48 05A20 05C10 05C38 05E99 15A45 47A50 47B49 BibTeX Cite \textit{S. M. Fallat} and \textit{P. K. Vishwakarma}, ``Inequalities for totally nonnegative matrices: Gantmacher--Krein, Karlin, and Laplace'', Preprint, arXiv:2305.16485 [math.CA] (2023) Full Text: arXiv OA License
Fallat, Shaun M.; Hall, H. Tracy; Levene, Rupert H.; Meyer, Seth A.; Nasserasr, Shahla; Oblak, Polona; Šmigoc, Helena Spectral arbitrariness for trees fails spectacularly. arXiv:2301.11073 Preprint, arXiv:2301.11073 [math.CO] (2023). MSC: 15A29 05C50 15A18 BibTeX Cite \textit{S. M. Fallat} et al., ``Spectral arbitrariness for trees fails spectacularly'', Preprint, arXiv:2301.11073 [math.CO] (2023) Full Text: arXiv OA License
Fallat, Shaun; Parenteau, Johnna Null vectors, Schur complements, and Parter vertices. (English) Zbl 1517.15009 Involve 15, No. 5, 843-856 (2022). Reviewer: Juan Ramón Torregrosa Sánchez (Valencia) MSC: 15A29 15A18 05C50 05C05 PDFBibTeX XMLCite \textit{S. Fallat} and \textit{J. Parenteau}, Involve 15, No. 5, 843--856 (2022; Zbl 1517.15009) Full Text: DOI
Fallat, Shaun M.; Hall, H. Tracy; Lin, Jephian C.-H.; Shader, Bryan L. The bifurcation lemma for strong properties in the inverse eigenvalue problem of a graph. (English) Zbl 1490.05158 Linear Algebra Appl. 648, 70-87 (2022). MSC: 05C50 15A18 15B35 15B57 58C15 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Linear Algebra Appl. 648, 70--87 (2022; Zbl 1490.05158) Full Text: DOI arXiv
Fallat, Shaun; Mojallal, Seyed Ahmad On the minimum number of distinct eigenvalues of a threshold graph. (English) Zbl 1487.05158 Linear Algebra Appl. 642, 1-29 (2022). MSC: 05C50 05C30 15A29 15A18 PDFBibTeX XMLCite \textit{S. Fallat} and \textit{S. A. Mojallal}, Linear Algebra Appl. 642, 1--29 (2022; Zbl 1487.05158) Full Text: DOI arXiv
Fallat, Shaun M.; Tifenbach, Ryan M. Sums of rank-one matrices and ranks of principal submatrices. (English) Zbl 1461.15001 Linear Multilinear Algebra 69, No. 1, 9-18 (2021). Reviewer: John D. Dixon (Ottawa) MSC: 15A03 15B57 15A15 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{R. M. Tifenbach}, Linear Multilinear Algebra 69, No. 1, 9--18 (2021; Zbl 1461.15001) Full Text: DOI
Fallat, Shaun; Johnson, Charles R.; Sokal, Alan D. Corrigendum to: “Total positivity of sums, Hadamard products and Hadamard powers: results and counterexamples”. (English) Zbl 1475.15041 Linear Algebra Appl. 613, 393-396 (2021). Reviewer: Luyining Gan (Reno) MSC: 15B48 15B05 44A60 PDFBibTeX XMLCite \textit{S. Fallat} et al., Linear Algebra Appl. 613, 393--396 (2021; Zbl 1475.15041) Full Text: DOI
Adm, Mohammad; Almuhtaseb, Khawla; Fallat, Shaun; Meagher, Karen; Nasserasr, Shahla; Shirazi, Mahsa N.; Razafimahatratra, A. S. Weakly Hadamard diagonalizable graphs. (English) Zbl 1458.05136 Linear Algebra Appl. 610, 86-119 (2021). MSC: 05C50 15A18 05B20 05E30 PDFBibTeX XMLCite \textit{M. Adm} et al., Linear Algebra Appl. 610, 86--119 (2021; Zbl 1458.05136) Full Text: DOI
Adm, Mohammad; Fallat, Shaun; Meagher, Karen; Nasserasr, Shahla; Plosker, Sarah; Yang, Boting Corrigendum to: “Achievable multiplicity partitions in the inverse eigenvalue problem of a graph”. (English) Zbl 1470.05098 Spec. Matrices 8, 235-241 (2020). MSC: 05C50 15A18 PDFBibTeX XMLCite \textit{M. Adm} et al., Spec. Matrices 8, 235--241 (2020; Zbl 1470.05098) Full Text: DOI
Fallat, Shaun M.; Martínez-Rivera, Xavier On the almost-principal minors of a symmetric matrix. (English) Zbl 1468.15004 Linear Algebra Appl. 606, 219-243 (2020). Reviewer: Ian M. Wanless (Clayton) MSC: 15A15 15A03 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{X. Martínez-Rivera}, Linear Algebra Appl. 606, 219--243 (2020; Zbl 1468.15004) Full Text: DOI arXiv
Chan, Ada; Fallat, Shaun; Kirkland, Steve; Lin, Jephian C.-H.; Nasserasr, Shahla; Plosker, Sarah Complex Hadamard diagonalisable graphs. (English) Zbl 1446.05055 Linear Algebra Appl. 605, 158-179 (2020). MSC: 05C50 05C76 05C25 05B20 15A18 81P45 PDFBibTeX XMLCite \textit{A. Chan} et al., Linear Algebra Appl. 605, 158--179 (2020; Zbl 1446.05055) Full Text: DOI arXiv
Barrett, Wayne; Butler, Steve; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; Lin, Jephian C.-H.; Shader, Bryan L.; Young, Michael The inverse eigenvalue problem of a graph: multiplicities and minors. (English) Zbl 1436.05059 J. Comb. Theory, Ser. B 142, 276-306 (2020). MSC: 05C50 05C83 15A18 15A29 PDFBibTeX XMLCite \textit{W. Barrett} et al., J. Comb. Theory, Ser. B 142, 276--306 (2020; Zbl 1436.05059) Full Text: DOI arXiv
Adm, Mohammad; Fallat, Shaun; Meagher, Karen; Nasserasr, Shahla; Plosker, Sarah; Yang, Boting Achievable multiplicity partitions in the inverse eigenvalue problem of a graph. (English) Zbl 1431.05097 Spec. Matrices 7, 276-290 (2019); corrigendum ibid. 8, 235-241 (2020). MSC: 05C50 15A18 PDFBibTeX XMLCite \textit{M. Adm} et al., Spec. Matrices 7, 276--290 (2019; Zbl 1431.05097) Full Text: DOI arXiv
Fallat, Shaun M.; Martínez-Rivera, Xavier The quasi principal rank characteristic sequence. (English) Zbl 1390.15122 Linear Algebra Appl. 548, 42-56 (2018). MSC: 15B57 15A15 15A03 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{X. Martínez-Rivera}, Linear Algebra Appl. 548, 42--56 (2018; Zbl 1390.15122) Full Text: DOI arXiv
Adm, Mohammad; Al Muhtaseb, Khawla; Ghani, Ayed Abedel; Fallat, Shaun; Garloff, Jürgen Further applications of the Cauchon algorithm to rank determination and bidiagonal factorization. (English) Zbl 1386.15031 Linear Algebra Appl. 545, 240-255 (2018). MSC: 15A23 15A03 PDFBibTeX XMLCite \textit{M. Adm} et al., Linear Algebra Appl. 545, 240--255 (2018; Zbl 1386.15031) Full Text: DOI Link
Fallat, Shaun; Lauritzen, Steffen; Sadeghi, Kayvan; Uhler, Caroline; Wermuth, Nanny; Zwiernik, Piotr Total positivity in Markov structures. (English) Zbl 1414.60010 Ann. Stat. 45, No. 3, 1152-1184 (2017). MSC: 60E15 62H99 15B48 PDFBibTeX XMLCite \textit{S. Fallat} et al., Ann. Stat. 45, No. 3, 1152--1184 (2017; Zbl 1414.60010) Full Text: DOI arXiv Euclid
Barrett, Wayne; Fallat, Shaun; Hall, H. Tracy; Hogben, Leslie; Lin, Jephian C.-H.; Shader, Bryan L. Generalizations of the strong Arnold property and the minimum number of distinct eigenvalues of a graph. (English) Zbl 1366.05065 Electron. J. Comb. 24, No. 2, Research Paper P2.40, 28 p. (2017). MSC: 05C50 15A18 15A29 15B57 58C15 PDFBibTeX XMLCite \textit{W. Barrett} et al., Electron. J. Comb. 24, No. 2, Research Paper P2.40, 28 p. (2017; Zbl 1366.05065) Full Text: arXiv Link
Fallat, Shaun; Johnson, Charles R.; Sokal, Alan D. Total positivity of sums, Hadamard products and Hadamard powers: results and counterexamples. (English) Zbl 1359.15027 Linear Algebra Appl. 520, 242-259 (2017); corrigendum ibid. 613, 393-396 (2021). MSC: 15B48 15B05 44A60 PDFBibTeX XMLCite \textit{S. Fallat} et al., Linear Algebra Appl. 520, 242--259 (2017; Zbl 1359.15027) Full Text: DOI arXiv
Fallat, Shaun (ed.); Nasserasr, Shahla (ed.); Wang, Qing-Wen (ed.); Zhang, Fuzhen (ed.) Editors’ summary of the special issue dedicated to the 5th international conference on matrix analysis and applications. (English) Zbl 1354.00095 Spec. Matrices 4, 366-367 (2016). MSC: 00B25 15-06 PDFBibTeX XMLCite \textit{S. Fallat} (ed.) et al., Spec. Matrices 4, 366--367 (2016; Zbl 1354.00095) Full Text: DOI
Fallat, Shaun; Soltani, Abolghasem Line graphs: their maximum nullities and zero forcing numbers. (English) Zbl 1413.05225 Czech. Math. J. 66, No. 3, 743-755 (2016). Reviewer: C. M. da Fonseca (Safat) MSC: 05C50 15A18 15A03 05C76 PDFBibTeX XMLCite \textit{S. Fallat} and \textit{A. Soltani}, Czech. Math. J. 66, No. 3, 743--755 (2016; Zbl 1413.05225) Full Text: DOI Link
Fallat, Shaun M.; Olesky, Dale D.; van den Driessche, Pauline The enhanced principal rank characteristic sequence for skew-symmetric matrices. (English) Zbl 1334.15018 Linear Algebra Appl. 498, 366-377 (2016). MSC: 15A15 15A03 15B57 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Linear Algebra Appl. 498, 366--377 (2016; Zbl 1334.15018) Full Text: DOI
Butler, Steve; Catral, Minerva; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; van den Driessche, P.; Young, Michael The enhanced principal rank characteristic sequence. (English) Zbl 1334.15017 Linear Algebra Appl. 498, 181-200 (2016). MSC: 15A15 15A03 15B57 05C50 PDFBibTeX XMLCite \textit{S. Butler} et al., Linear Algebra Appl. 498, 181--200 (2016; Zbl 1334.15017) Full Text: DOI
Barrett, Wayne; Butler, Steve; Catral, Minerva; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; Young, Michael The maximum nullity of a complete subdivision graph is equal to its zero forcing number. (English) Zbl 1320.05069 Electron. J. Linear Algebra 27, 444-457 (2014). MSC: 05C50 15A03 15A18 15B57 PDFBibTeX XMLCite \textit{W. Barrett} et al., Electron. J. Linear Algebra 27, 444--457 (2014; Zbl 1320.05069)
Barrett, Wayne; Butler, Steve; Catral, Minerva; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; van den Driessche, P.; Young, Michael The principal rank characteristic sequence over various fields. (English) Zbl 1297.15002 Linear Algebra Appl. 459, 222-236 (2014). MSC: 15A03 15A15 15A18 15B57 05C50 PDFBibTeX XMLCite \textit{W. Barrett} et al., Linear Algebra Appl. 459, 222--236 (2014; Zbl 1297.15002) Full Text: DOI
Taklimi, Fatemeh Alinaghipour; Fallat, Shaun; Meagher, Karen On the relationships between zero forcing numbers and certain graph coverings. (English) Zbl 1291.05126 Spec. Matrices 2, No. 1, 30-45 (2014). MSC: 05C50 05C70 15B35 PDFBibTeX XMLCite \textit{F. A. Taklimi} et al., Spec. Matrices 2, 30--45 (2014; Zbl 1291.05126) Full Text: DOI arXiv
Barrett, Wayne; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie Note on Nordhaus-Gaddum problems for Colin de Verdière type parameters. (English) Zbl 1295.05140 Electron. J. Comb. 20, No. 3, Research Paper P56, 9 p. (2013). MSC: 05C50 05C40 05C83 15A03 15B57 PDFBibTeX XMLCite \textit{W. Barrett} et al., Electron. J. Comb. 20, No. 3, Research Paper P56, 9 p. (2013; Zbl 1295.05140)
Ahmadi, Bahman; Alinaghipour, Fatemeh; Cavers, Michael S.; Fallat, Shaun; Meagher, Karen; Nasser, Shahla Minimum number of distinct eigenvalues of graphs. (English) Zbl 1282.05085 Electron. J. Linear Algebra 26, 673-691 (2013). MSC: 05C50 15A18 05C05 PDFBibTeX XMLCite \textit{B. Ahmadi} et al., Electron. J. Linear Algebra 26, 673--691 (2013; Zbl 1282.05085) Full Text: DOI arXiv Link
Fallat, Shaun M.; Mitchell, Lon H. Colin de Verdière parameters of chordal graphs. (English) Zbl 1282.05112 Electron. J. Linear Algebra 26, 49-62 (2013). MSC: 05C50 15A18 05B20 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{L. H. Mitchell}, Electron. J. Linear Algebra 26, 49--62 (2013; Zbl 1282.05112) Full Text: DOI
Fallat, Shaun M.; Nasserasr, Shahla On the null space structure associated with trees and cycles. (English) Zbl 1274.05290 J. Comb. Math. Comb. Comput. 85, 253-272 (2013). MSC: 05C50 15A18 05C05 05C38 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{S. Nasserasr}, J. Comb. Math. Comb. Comput. 85, 253--272 (2013; Zbl 1274.05290)
Barioli, Francesco; Barrett, Wayne; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; Shader, Bryan; Den Driessche, P. Van; Van Der Holst, Hein Parameters related to tree-width, zero forcing, and maximum nullity of a graph. (English) Zbl 1259.05112 J. Graph Theory 72, No. 1-2, 146-177 (2013). MSC: 05C50 05C85 05C83 15A03 15A18 05C40 05C75 68R10 PDFBibTeX XMLCite \textit{F. Barioli} et al., J. Graph Theory 72, No. 1--2, 146--177 (2013; Zbl 1259.05112) Full Text: DOI
Fan, Yi-Zheng; Fallat, Shaun Edge bipartiteness and signless Laplacian spread of graphs. (English) Zbl 1289.05281 Appl. Anal. Discrete Math. 6, No. 1, 31-45 (2012). Reviewer: Bojana Borovićanin (Kragujevac) MSC: 05C50 15A18 PDFBibTeX XMLCite \textit{Y.-Z. Fan} and \textit{S. Fallat}, Appl. Anal. Discrete Math. 6, No. 1, 31--45 (2012; Zbl 1289.05281) Full Text: DOI
Fallat, Shaun M.; Xing, YongJun On the spread of certain normal matrices. (English) Zbl 1256.15005 Linear Multilinear Algebra 60, No. 11-12, 1391-1407 (2012). MSC: 15A18 15A03 15B57 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{Y. Xing}, Linear Multilinear Algebra 60, No. 11--12, 1391--1407 (2012; Zbl 1256.15005) Full Text: DOI Link
Cavers, Michael S.; Fallat, Shaun M. Allow problems concerning spectral properties of patterns. (English) Zbl 1251.15034 Electron. J. Linear Algebra 23, 731-754 (2012). MSC: 15B35 15A18 15A29 05C50 PDFBibTeX XMLCite \textit{M. S. Cavers} and \textit{S. M. Fallat}, Electron. J. Linear Algebra 23, 731--754 (2012; Zbl 1251.15034) Full Text: DOI Link
Ahmadi, B.; Alinaghipour, F.; Fallat, Shaun M.; Fan, Yi-Zheng; Meagher, K.; Nasserasr, S. The minimum rank of universal adjacency matrices. (English) Zbl 1252.05107 Linear Algebra Appl. 437, No. 8, 2064-2076 (2012). MSC: 05C50 05C38 15A03 15A18 15A27 PDFBibTeX XMLCite \textit{B. Ahmadi} et al., Linear Algebra Appl. 437, No. 8, 2064--2076 (2012; Zbl 1252.05107) Full Text: DOI arXiv
Barioli, Francesco; Barrett, Wayne; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; van der Holst, Hein On the graph complement conjecture for minimum rank. (English) Zbl 1241.05064 Linear Algebra Appl. 436, No. 12, 4373-4391 (2012). MSC: 05C50 15A03 15B57 15A18 PDFBibTeX XMLCite \textit{F. Barioli} et al., Linear Algebra Appl. 436, No. 12, 4373--4391 (2012; Zbl 1241.05064) Full Text: DOI
Fallat, Shaun; Fan, Yi-Zheng Bipartiteness and the least eigenvalue of signless Laplacian of graphs. (English) Zbl 1244.05142 Linear Algebra Appl. 436, No. 9, 3254-3267 (2012). MSC: 05C50 15A18 05C70 PDFBibTeX XMLCite \textit{S. Fallat} and \textit{Y.-Z. Fan}, Linear Algebra Appl. 436, No. 9, 3254--3267 (2012; Zbl 1244.05142) Full Text: DOI
Brualdi, R. (ed.); Fallat, S. (ed.); Hogben, L. (ed.); Shader, B. (ed.); van den Driessche, P. (ed.) Special issue: Matrices described by patterns. Selected papers based on the presentations at the workshop, BIRS, Banff, Canada. (English) Zbl 1246.15002 Linear Algebra Appl. 436, No. 12, 4349-4529 (2012). MSC: 15-06 15A99 15B99 65F99 00B25 PDFBibTeX XML
Barik, S.; Fallat, S.; Kirkland, S. On Hadamard diagonalizable graphs. (English) Zbl 1221.05228 Linear Algebra Appl. 435, No. 8, 1885-1902 (2011). MSC: 05C50 15A18 PDFBibTeX XMLCite \textit{S. Barik} et al., Linear Algebra Appl. 435, No. 8, 1885--1902 (2011; Zbl 1221.05228) Full Text: DOI
Fallat, Shaun M.; Johnson, Charles R. Totally nonnegative matrices. (English) Zbl 1390.15001 Princeton Series in Applied Mathematics. Princeton, NJ: Princeton University Press (ISBN 978-0-691-12157-4/hbk). xv, 248 p. (2011). MSC: 15-02 15B48 15A45 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{C. R. Johnson}, Totally nonnegative matrices. Princeton, NJ: Princeton University Press (2011; Zbl 1390.15001)
Barioli, Francesco; Fallat, Shaun M.; Mitchell, Lon H.; Narayan, Sivaram K. Minimum semidefinite rank of outerplanar graphs and the tree cover number. (English) Zbl 1205.05135 Electron. J. Linear Algebra 22, 10-21 (2011). MSC: 05C50 15A03 15A18 PDFBibTeX XMLCite \textit{F. Barioli} et al., Electron. J. Linear Algebra 22, 10--21 (2011; Zbl 1205.05135) Full Text: DOI EuDML EMIS
Barioli, Francesco; Barrett, Wayne; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; Shader, Bryan; van den Driessche, P.; van der Holst, Hein Zero forcing parameters and minimum rank problems. (English) Zbl 1209.05139 Linear Algebra Appl. 433, No. 2, 401-411 (2010). MSC: 05C50 15A03 15A18 15B57 PDFBibTeX XMLCite \textit{F. Barioli} et al., Linear Algebra Appl. 433, No. 2, 401--411 (2010; Zbl 1209.05139) Full Text: DOI arXiv Link
Cavers, Michael; Fallat, Shaun; Kirkland, Steve On the normalized Laplacian energy and general Randić index \(R_{-1}\) of graphs. (English) Zbl 1217.05138 Linear Algebra Appl. 433, No. 1, 172-190 (2010). MSC: 05C50 05C90 15A18 15A42 PDFBibTeX XMLCite \textit{M. Cavers} et al., Linear Algebra Appl. 433, No. 1, 172--190 (2010; Zbl 1217.05138) Full Text: DOI
Barioli, Francesco; Fallat, Shaun M.; Hall, H. Tracy; Hershkowitz, Daniel; Hogben, Leslie; Van Der Holst, Hein; Shader, Bryan On the minimum rank of not necessarily symmetric matrices: a preliminary study. (English) Zbl 1169.05345 Electron. J. Linear Algebra 18, 126-145 (2009). MSC: 05C50 05C05 15A03 15A18 PDFBibTeX XMLCite \textit{F. Barioli} et al., Electron. J. Linear Algebra 18, 126--145 (2009; Zbl 1169.05345) Full Text: DOI EuDML EMIS Link
Liu, Xiao Ping; Fallat, Shaun M. Multiplicative principal-minor inequalities for a class of oscillatory matrices. (English) Zbl 1166.15009 JIPAM, J. Inequal. Pure Appl. Math. 9, No. 4, Paper No. 92, 18 p. (2008). Reviewer: John D. Dixon (Ottawa) MSC: 15A45 15B48 15A15 PDFBibTeX XMLCite \textit{X. P. Liu} and \textit{S. M. Fallat}, JIPAM, J. Inequal. Pure Appl. Math. 9, No. 4, Paper No. 92, 18 p. (2008; Zbl 1166.15009) Full Text: EuDML EMIS
Barioli, Francesco; Fallat, Shaun M.; Smith, Ronald L. On acyclic and unicyclic graphs whose minimum rank equals the diameter. (English) Zbl 1145.05036 Linear Algebra Appl. 429, No. 7, 1568-1578 (2008). MSC: 05C50 15A03 15B57 PDFBibTeX XMLCite \textit{F. Barioli} et al., Linear Algebra Appl. 429, No. 7, 1568--1578 (2008; Zbl 1145.05036) Full Text: DOI
Barioli, Francesco; Barrett, Wayne; Butler, Steve; Ciobă, Sebastian M.; Cvetković, Dragos; Fallat, Shaun M.; Godsil, Chris; Haemers, Willem; Hogben, Leslie; Mikkelson, Rana; Narayan, Sivaram; Pryporova, Olga; Sciriha, Irene; So, Wasin; Stevanović, Dragan; van der Holst, Hein; Vander Meulen, Kevin; Wehe, Amy Wangsness Zero forcing sets and the minimum rank of graphs. (English) Zbl 1135.05035 Linear Algebra Appl. 428, No. 7, 1628-1648 (2008). MSC: 05C50 15A18 15A03 PDFBibTeX XMLCite \textit{F. Barioli} et al., Linear Algebra Appl. 428, No. 7, 1628--1648 (2008; Zbl 1135.05035) Full Text: DOI Link
Fallat, Shaun M.; Woerdeman, Hugo J. Refinements on the interlacing of eigenvalues of certain totally nonnegative matrices. (English) Zbl 1145.15009 Oper. Matrices 1, No. 2, 271-281 (2007). Reviewer: Mariano Gasca (Zaragoza) MSC: 15A18 15B48 42C05 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{H. J. Woerdeman}, Oper. Matrices 1, No. 2, 271--281 (2007; Zbl 1145.15009) Full Text: DOI
Fallat, Shaun; Liu, Xiao Ping A new type of factorization of oscillatory matrices. (English) Zbl 1135.15008 Int. J. Pure Appl. Math. 37, No. 2, 271-296 (2007). Reviewer: A. Arvanitoyeorgos (Rion) MSC: 15A23 15B48 PDFBibTeX XMLCite \textit{S. Fallat} and \textit{X. P. Liu}, Int. J. Pure Appl. Math. 37, No. 2, 271--296 (2007; Zbl 1135.15008)
Fallat, Shaun M.; Johnson, Charles R. Hadamard duals retractability and Oppenheim’s inequality. (English) Zbl 1137.15009 Oper. Matrices 1, No. 3, 369-383 (2007). Reviewer: Fozi Dannan (Damascus) MSC: 15A45 15B48 15B57 15A15 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{C. R. Johnson}, Oper. Matrices 1, No. 3, 369--383 (2007; Zbl 1137.15009) Full Text: DOI
Fallat, Shaun M.; Hogben, Leslie The minimum rank of symmetric matrices described by a graph: a survey. (English) Zbl 1122.05057 Linear Algebra Appl. 426, No. 2-3, 558-582 (2007). MSC: 05C50 15A03 15A18 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{L. Hogben}, Linear Algebra Appl. 426, No. 2--3, 558--582 (2007; Zbl 1122.05057) Full Text: DOI arXiv
Fallat, Shaun; Liu, Xiao Ping A class of oscillatory matrices with exponent \(n - 1\). (English) Zbl 1122.15010 Linear Algebra Appl. 424, No. 2-3, 466-479 (2007). Reviewer: Yueh-er Kuo (Knoxville) MSC: 15A15 15B48 PDFBibTeX XMLCite \textit{S. Fallat} and \textit{X. P. Liu}, Linear Algebra Appl. 424, No. 2--3, 466--479 (2007; Zbl 1122.15010) Full Text: DOI
Fallat, Shaun M.; Johnson, Charles R. Hadamard powers and totally positive matrices. (English) Zbl 1123.15014 Linear Algebra Appl. 423, No. 2-3, 420-427 (2007). Reviewer: Mariano Gasca (Zaragoza) MSC: 15B48 15A15 15B57 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{C. R. Johnson}, Linear Algebra Appl. 423, No. 2--3, 420--427 (2007; Zbl 1123.15014) Full Text: DOI
Barioli, Francesco; Fallat, Shaun On the minimum rank of the join of graphs and decomposable graphs. (English) Zbl 1112.05061 Linear Algebra Appl. 421, No. 2-3, 252-263 (2007). MSC: 05C50 15A03 15A18 PDFBibTeX XMLCite \textit{F. Barioli} and \textit{S. Fallat}, Linear Algebra Appl. 421, No. 2--3, 252--263 (2007; Zbl 1112.05061) Full Text: DOI
Fallat, Shaun M.; Herman, Allen; Gekhtman, Michael I.; Johnson, Charles R. Compressions of totally positive matrices. (English) Zbl 1112.15024 SIAM J. Matrix Anal. Appl. 28, No. 1, 68-80 (2006). Reviewer: Juan Ramon Torregrosa Sanchez (Valencia) MSC: 15B48 15A15 05C50 15A45 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., SIAM J. Matrix Anal. Appl. 28, No. 1, 68--80 (2006; Zbl 1112.15024) Full Text: DOI
Barioli, Francesco; Fallat, Shaun; Hogben, Leslie A variant on the graph parameters of Colin de Verdière: implications to the minimum rank of graphs. (English) Zbl 1092.05042 Electron. J. Linear Algebra 13, 387-404 (2005). MSC: 05C50 15A18 PDFBibTeX XMLCite \textit{F. Barioli} et al., Electron. J. Linear Algebra 13, 387--404 (2005; Zbl 1092.05042) Full Text: DOI EuDML EMIS
Barioli, Francesco; Fallat, Shaun; Hogben, Leslie On the difference between the maximum multiplicity and path cover number for tree-like graphs. (English) Zbl 1072.05037 Linear Algebra Appl. 409, 13-31 (2005). MSC: 05C50 15A18 PDFBibTeX XMLCite \textit{F. Barioli} et al., Linear Algebra Appl. 409, 13--31 (2005; Zbl 1072.05037) Full Text: DOI
Barioli, Francesco; Fallat, Shaun On the eigenvalues of generalized and double generalized stars. (English) Zbl 1082.15015 Linear Multilinear Algebra 53, No. 4, 269-291 (2005). Reviewer: Jaspal Singh Aujla (Jalandhar) MSC: 15A18 05C50 PDFBibTeX XMLCite \textit{F. Barioli} and \textit{S. Fallat}, Linear Multilinear Algebra 53, No. 4, 269--291 (2005; Zbl 1082.15015) Full Text: DOI
Fallat, Shaun M.; Gekhtman, Michael I. Jordan structures of totally nonnegative matrices. (English) Zbl 1072.15029 Can. J. Math. 57, No. 1, 82-98 (2005). Reviewer: John D. Dixon (Ottawa) MSC: 15B48 15A21 05C38 05C50 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{M. I. Gekhtman}, Can. J. Math. 57, No. 1, 82--98 (2005; Zbl 1072.15029) Full Text: DOI
Fallat, Shaun M. A remark on oscillatory matrices. (English) Zbl 1084.15012 Linear Algebra Appl. 393, 139-147 (2004). Reviewer: Valeriu Prepeliţă (Bucureşti) MSC: 15A23 15B48 05C50 05C38 PDFBibTeX XMLCite \textit{S. M. Fallat}, Linear Algebra Appl. 393, 139--147 (2004; Zbl 1084.15012) Full Text: DOI
Barioli, Francesco; Fallat, Shaun; Hogben, Leslie Computation of minimal rank and path cover number for certain graphs. (English) Zbl 1052.05045 Linear Algebra Appl. 392, 289-303 (2004). MSC: 05C50 15A18 PDFBibTeX XMLCite \textit{F. Barioli} et al., Linear Algebra Appl. 392, 289--303 (2004; Zbl 1052.05045) Full Text: DOI
Barioli, Francesco; Fallat, Shaun M. On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices. (English) Zbl 1055.15010 Electron. J. Linear Algebra 11, 41-50 (2004). Reviewer: E. Kreyszig (Ottawa) MSC: 15A18 15B48 05C50 15A29 PDFBibTeX XMLCite \textit{F. Barioli} and \textit{S. M. Fallat}, Electron. J. Linear Algebra 11, 41--50 (2004; Zbl 1055.15010) Full Text: DOI EuDML EMIS Link
Fallat, Shaun M.; Kirkland, Steve; Pati, Sukanta Maximizing algebraic connectivity over unicyclic graphs. (English) Zbl 1043.05074 Linear Multilinear Algebra 51, No. 3, 221-241 (2003). MSC: 05C50 15A18 15B48 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Linear Multilinear Algebra 51, No. 3, 221--241 (2003; Zbl 1043.05074) Full Text: DOI
Fallat, Shaun M.; Kirkland, Steve; Pati, Sukanta On graphs with algebraic connectivity equal to minimum edge density. (English) Zbl 1026.05075 Linear Algebra Appl. 373, 31-50 (2003). MSC: 05C50 15A18 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Linear Algebra Appl. 373, 31--50 (2003; Zbl 1026.05075) Full Text: DOI
Fallat, Shaun M.; Gekhtman, Michael I.; Johnson, Charles R. Multiplicative principal-minor inequalities for totally nonnegative matrices. (English) Zbl 1030.15021 Adv. Appl. Math. 30, No. 3, 442-470 (2003). Reviewer: Martin Argerami (Regina) MSC: 15A45 15A15 15B48 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Adv. Appl. Math. 30, No. 3, 442--470 (2003; Zbl 1030.15021) Full Text: DOI
Fallat, Shaun M.; Fiedler, Miroslav; Markham, Thomas L. Generalized oscillatory matrices. (English) Zbl 1026.15008 Linear Algebra Appl. 359, No. 1-3, 79-90 (2003). Reviewer: Alexander Guterman (Moskva) MSC: 15A23 15B33 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Linear Algebra Appl. 359, No. 1--3, 79--90 (2003; Zbl 1026.15008) Full Text: DOI
Fallat, Shaun M.; Tsatsomeros, Michael J. On the Cayley transform of positivity classes of matrices. (English) Zbl 1023.15009 Electron. J. Linear Algebra 9, 190-196 (2002). Reviewer: Rodica Covaci (Cluj-Napoca) MSC: 15B48 15A23 15A24 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{M. J. Tsatsomeros}, Electron. J. Linear Algebra 9, 190--196 (2002; Zbl 1023.15009) Full Text: DOI EuDML EMIS
Cheung, Wai-Shun; Fallat, Shaun; Li, Chi-Kwong Multiplicative preservers on semigroups of matrices. (English) Zbl 1025.15001 Linear Algebra Appl. 355, No. 1-3, 173-186 (2002). Reviewer: John D.Dixon (Ottawa / Ontario) MSC: 15A04 15A30 15B48 15B57 PDFBibTeX XMLCite \textit{W.-S. Cheung} et al., Linear Algebra Appl. 355, No. 1--3, 173--186 (2002; Zbl 1025.15001) Full Text: DOI
Fallat, Shaun M.; Kirkland, Steve; Pati, Sukanta Minimizing algebraic connectivity over connected graphs with fixed girth. (English) Zbl 0995.05092 Discrete Math. 254, No. 1-3, 115-142 (2002). Reviewer: Dragan Stevanović (Niš) MSC: 05C50 15A18 15B48 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Discrete Math. 254, No. 1--3, 115--142 (2002; Zbl 0995.05092) Full Text: DOI
Fallat, Shaun M. Bidiagonal factorizations of totally nonnegative matrices. (English) Zbl 1032.15015 Am. Math. Mon. 108, No. 8, 697-712 (2001). Reviewer: Adhemar Bultheel (Leuven) MSC: 15B48 15A23 PDFBibTeX XMLCite \textit{S. M. Fallat}, Am. Math. Mon. 108, No. 8, 697--712 (2001; Zbl 1032.15015) Full Text: DOI
Fallat, Shaun M.; Johnson, Charles R. Multiplicative principal-minor inequalities for tridiagonal sign-symmetric \(P\)-matrices. (English) Zbl 0986.15017 Taiwanese J. Math. 5, No. 3, 655-665 (2001). Reviewer: Václav Burjan (Praha) MSC: 15A45 15A15 15B48 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{C. R. Johnson}, Taiwanese J. Math. 5, No. 3, 655--665 (2001; Zbl 0986.15017) Full Text: DOI
Crans, Alissa S.; Fallat, Shaun M.; Johnson, Charles R. The Hadamard core of the totally nonnegative matrices. (English) Zbl 0989.15009 Linear Algebra Appl. 328, No. 1-3, 203-222 (2001). Reviewer: Václav Burjan (Praha) MSC: 15B48 PDFBibTeX XMLCite \textit{A. S. Crans} et al., Linear Algebra Appl. 328, No. 1--3, 203--222 (2001; Zbl 0989.15009) Full Text: DOI
Fallat, Shaun M.; Neumann, Michael On Perron complements of totally nonnegative matrices. (English) Zbl 0977.15012 Linear Algebra Appl. 327, No. 1-3, 85-94 (2001). Reviewer: Václav Burjan (Praha) MSC: 15B48 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{M. Neumann}, Linear Algebra Appl. 327, No. 1--3, 85--94 (2001; Zbl 0977.15012) Full Text: DOI
Fallat, Shaun M.; Gekhtman, Michael I.; Johnson, Charles R. Spectral structures of irreducible totally nonnegative matrices. (English) Zbl 0970.15013 SIAM J. Matrix Anal. Appl. 22, No. 2, 627-645 (2000). Reviewer: Yueh-er Kuo (Knoxville) MSC: 15B48 15A18 15A21 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., SIAM J. Matrix Anal. Appl. 22, No. 2, 627--645 (2000; Zbl 0970.15013) Full Text: DOI
Fallat, Shaun M.; Johnson, Charles R. Determinantal inequalities: Ancient history and recent advances. (English) Zbl 0965.15022 Huynh, D. V. (ed.) et al., Algebra and its applications. Proceedings of the international conference, Athens, OH, USA, March 25-28, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 259, 199-212 (2000). MSC: 15A45 15A15 15A42 15B48 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{C. R. Johnson}, Contemp. Math. 259, 199--212 (2000; Zbl 0965.15022)
Fallat, Shaun M.; van den Driessche, P. On matrices with all minors negative. (English) Zbl 0962.15014 Electron. J. Linear Algebra 7, 92-99 (2000). Reviewer: Arnold Richard Kräuter (Leoben) MSC: 15B48 15A18 65F05 15A09 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{P. van den Driessche}, Electron. J. Linear Algebra 7, 92--99 (2000; Zbl 0962.15014) Full Text: EuDML EMIS
Fallat, Shaun; Johnson, Charles R.; Markham, Thomas L. Eigenvalues of products of matrices and submatrices in certain positivity classes. (English) Zbl 0965.15017 Linear Multilinear Algebra 47, No. 3, 235-248 (2000). Reviewer: Michal Zajac (Bratislava) MSC: 15A42 15B48 PDFBibTeX XMLCite \textit{S. Fallat} et al., Linear Multilinear Algebra 47, No. 3, 235--248 (2000; Zbl 0965.15017) Full Text: DOI
Fallat, Shaun M.; Johnson, Charles R.; Torregrosa, Juan R.; Urbano, Ana M. \(P\)-matrix completions under weak symmetry assumptions. (English) Zbl 0963.15021 Linear Algebra Appl. 312, No. 1-3, 73-91 (2000). Reviewer: Rodica Covaci (Cluj-Napoca) MSC: 15B48 15A29 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Linear Algebra Appl. 312, No. 1--3, 73--91 (2000; Zbl 0963.15021) Full Text: DOI
Fallat, Shaun M.; Johnson, Charles R.; Smith, Ronald L. The general totally positive matrix completion problem with few unspecified entries. (English) Zbl 0941.15009 Electron. J. Linear Algebra 7, 1-20 (2000). Reviewer: G.Bonanno (Davis) MSC: 15A29 15B48 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Electron. J. Linear Algebra 7, 1--20 (2000; Zbl 0941.15009) Full Text: EuDML EMIS
Fallat, Shaun M.; Johnson, Charles R. Sub-direct sums and positivity classes of matrices. (English) Zbl 0973.15013 Linear Algebra Appl. 288, No. 1-3, 149-173 (1999). MSC: 15B48 PDFBibTeX XMLCite \textit{S. M. Fallat} and \textit{C. R. Johnson}, Linear Algebra Appl. 288, No. 1--3, 149--173 (1999; Zbl 0973.15013) Full Text: DOI
Fallat, Shaun M.; Johnson, Charles R.; Smith, Ronald L.; van den Driessche, P. Eigenvalue location for nonnegative and Z-matrices. (English) Zbl 0946.15013 Linear Algebra Appl. 277, No. 1-3, 187-198 (1998). Reviewer: E.Kreyszig (Ottawa) MSC: 15A42 15B48 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Linear Algebra Appl. 277, No. 1--3, 187--198 (1998; Zbl 0946.15013) Full Text: DOI
Johnson, Charles R.; Fallat, Shaun Olga, matrix theory and the Taussky unification problem. (English) Zbl 0946.15001 Linear Algebra Appl. 280, No. 1, 39-49 (1998). Reviewer: F.Uhlig (Auburn) MSC: 15-03 15B48 01A65 01A70 PDFBibTeX XMLCite \textit{C. R. Johnson} and \textit{S. Fallat}, Linear Algebra Appl. 280, No. 1, 39--49 (1998; Zbl 0946.15001) Full Text: DOI
Fallat, Shaun M.; Hall, H. Tracy; Johnson, Charles R. Characterization of product inequalities for principal minors of \(M\)-matrices and inverse \(M\)-matrices. (English) Zbl 0921.15012 Q. J. Math., Oxf. II. Ser. 49, No. 196, 451-458 (1998). Reviewer: K.H.Kim (Montgomery) MSC: 15A45 15B48 PDFBibTeX XMLCite \textit{S. M. Fallat} et al., Q. J. Math., Oxf. II. Ser. 49, No. 196, 451--458 (1998; Zbl 0921.15012)
Fallat, Shaun; Kirkland, Steve Extremizing algebraic connectivity subject to graph theoretic constraints. (English) Zbl 0913.05073 Electron. J. Linear Algebra 3, 48-74 (1998). Reviewer: B.Mohar (Ljubljana) MSC: 05C50 15B48 PDFBibTeX XMLCite \textit{S. Fallat} and \textit{S. Kirkland}, Electron. J. Linear Algebra 3, 48--74 (1998; Zbl 0913.05073) Full Text: DOI EuDML EMIS
Fallat, Shaun; Olesky, D. D.; van den Driessche, P. Graph theoretic aspects of maximizing the spectral radius of nonnegative matrices. (English) Zbl 0870.15011 Linear Algebra Appl. 253, 61-77 (1997). Reviewer: K.Burian (Havířov) MSC: 15A42 05C50 PDFBibTeX XMLCite \textit{S. Fallat} et al., Linear Algebra Appl. 253, 61--77 (1997; Zbl 0870.15011) Full Text: DOI Link
Fallat, Shaun; van den Driessche, P. Maximum determinant of \((0,1)\) matrices with certain constant row and column sums. (English) Zbl 0885.15003 Linear Multilinear Algebra 42, No. 4, 303-318 (1997). Reviewer: G.Bonanno (Davis) MSC: 15A15 15A45 05B20 05C50 15B36 PDFBibTeX XMLCite \textit{S. Fallat} and \textit{P. van den Driessche}, Linear Multilinear Algebra 42, No. 4, 303--318 (1997; Zbl 0885.15003) Full Text: DOI