Publications

• B. Curtis et al., The non-symmetric strong multiplicity property for sign patterns, Electron. J. Linear Algebra {\bf 41} (2025), 153–165.
• S. Klanderman et al., Determinants of Seidel tournament matrices, Linear Algebra Appl. {\bf 707} (2025), 126–151.
• Z. Li et al., Editorial note for the special issue in honor of Frank J. Hall, Spec. Matrices {\bf 12} (2024), Paper No. 20240022, 2 pp.
  A. Abiad et al., The inverse nullity pair problem and the strong nullity interlacing property, Linear Algebra Appl. {\bf 699} (2024), 539–568.
• Hogben, L; Lin J; Shader, B. {Inverse Eigenvalue Problems of Graphs,
  Zero Forcing and Applications.” Mathematical Surveys and Monographs Vol 270,
  American Mathematical Society, 2022.
• 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.
  Linear Algebra Appl. 648 (2022), 70–87.
• Cheon, Gi-Sang ; Curtis, Bryan ; Shader, Bryan . Riordan-Krylov matrices over an algebra.Linear Algebra Appl. 636 (2022), 93–114.
• Hogben, Leslie ; Lin, Jephian C.-H. ; Shader, Bryan L. The inverse eigenvalue problem of a graph. 50 years of combinatorics, graph theory, and computing,
  239–262, Discrete Math. Appl. (Boca Raton), CRC Press, Boca Raton, FL, [2020], 2020.
• Butler, Steve; Erickson, Craig; Fallat, Shaun; Hall, H. Tracy; Kroschel, Brenda; Lin, Jephian C.-H.; Shader, Bryan; Warnberg, Nathan; Yang, Boting. Properties of a q-analogue of zero forcing. Graphs Combin. 36 (2020), no. 5, 1401–1419.
• 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. J. Combin. Theory Ser. B 142 (2020), 276–306.
• Curtis, Bryan A.; Shader, Bryan L. Sign patterns of orthogonal matrices and the strong inner product property. Linear Algebra Appl. 592 (2020), 228–259.
• Fallat, Shaun M.; Hogben, Leslie; Lin, Jephian C.-H.; Shader, Bryan L. The inverse eigenvalue problem of a graph, zero forcing, and related parameters.
  Notices Amer. Math. Soc. 67 (2020), no. 2, 257–261.
• Ferrero, Daniela; Flagg, Mary; Hall, H. Tracy; Hogben, Leslie; Lin, Jephian C.-H.; Meyer, Seth A.; Nasserasr, Shahla; Shader, Bryan. Rigid linkages and partial zero forcing.
  Electron. J. Combin. 26 (2019), no. 2, Paper No. 2.43, 25 pp.
• Curtis, Bryan; Earl, Jonathan; Livingston, David; Shader, Bryan. Resolution of conjectures related to Lights Out! and Cartesian products.
  Electron. J. Linear Algebra 34 (2018), 718–724.
• Deng, Bo; Li, Xueliang; Shader, Bryan; So, Wasin. On the maximum skew spectral radius and minimum skew energy of tournaments.
  Linear Multilinear Algebra 66 (2018), no. 7, 1434–1441.
• Eastman, B.; Kim, I.-J.; Shader, B. L.; Vander Meulen, K. N. Corrigendum to “Companion matrix patterns” [Linear Algebra Appl. 463 (2014) 255–272] [MR3262399].
  Linear Algebra Appl. 538 (2018), 225–227.
• 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. Electron. J. Combin. 24 (2017), no. 2, Paper No. 2.40, 28 pp.
• Butler, Steve; Catral, Minerva; Hall, H. Tracy; Hogben, Leslie; Martínez-Rivera, Xavier; Shader, Bryan; van den Driessche, Pauline. The enhanced principal rank characteristic sequence for Hermitian matrices. Electron. J. Linear Algebra 32 (2017), 58–75.
• Kim, In-Jae; Shader, Bryan L.; Vander Meulen, Kevin N.; West, Matthew. Spectrally arbitrary pattern extensions.Linear Algebra Appl. 517 (2017), 120–128.
• Eastman, B.; Kim, I.-J.; Shader, B. L.; Vander Meulen, K. N. Companion matrix patterns.
  Linear Algebra Appl. 463 (2014), 255–272.
• Shader, Bryan; Shaked-Monderer, Naomi; Szyld, Daniel B. Nearly positive matrices.
  Linear Algebra Appl. 449 (2014), 520–544.
• Garnett, C.; Olesky, D. D.; Shader, B. L.; van den Driessche, P. Integrally normalizable matrices and zero-nonzero patterns.
  Linear Algebra Appl. 449 (2014), 132–153.
• Mallik, Sudipta; Shader, Bryan L. Classes of graphs with minimum skew rank 4.
  Linear Algebra Appl. 439 (2013), no. 11, 3643–3657.
• Monfared, Keivan Hassani; Shader, Bryan L. Construction of matrices with a given graph and prescribed interlaced spectral data.
  Linear Algebra Appl. 438 (2013), no. 11, 4348–4358.
• Nair, Reshmi; Shader, Bryan L. Acyclic matrices with a small number of distinct eigenvalues.
  Linear Algebra Appl. 438 (2013), no. 10, 4075–4089.
  Garnett, Colin; Shader, Bryan L. The nilpotent-centralizer method for spectrally arbitrary patterns. Linear Algebra Appl. 438 (2013), no. 10, 3836–3850.
• Kim, In-Jae; Shader, Bryan L. Unordered multiplicity lists of a class of binary trees.
  Linear Algebra Appl. 438 (2013), no. 10, 3781–3788.
• Barioli, Francesco; Barrett, Wayne; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; Shader, Bryan; van den Driessche, P.; van der Holst, Hein. Parameters related to tree-width, zero forcing, and maximum nullity of a graph.
  J. Graph Theory 72 (2013), no. 2, 146–177.
• Garnett, Colin; Shader, Bryan L. A proof of the Tn conjecture: centralizers, Jacobians and spectrally arbitrary sign patterns. Linear Algebra Appl. 436 (2012), no. 12, 4451–4458.
• Allison, Mary; Shader, Bryan L. Fastest mixing Markov chain problem for the union of two cliques. Linear Multilinear Algebra 59 (2011), no. 7, 801–823.
• Doering, E.; Michael, T. S.; Shader, B. L. Even and odd tournament matrices with minimum rank over finite fields. Electron. J. Linear Algebra 22 (2011), 363–377.
• 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. Linear Algebra Appl. 433 (2010), no. 2, 401–411.
• Hall, H. Tracy; Hogben, Leslie; Martin, Ryan; Shader, Bryan. Expected values of parameters associated with the minimum rank of a graph.
  Linear Algebra Appl. 433 (2010), no. 1, 101–117.
• Deschamp, Brent J.; Shader, Bryan L. Permanents of Hessenberg (0,1)-matrices revisited.
  Electron. J. Linear Algebra 20 (2010), 20–52.
• Hogben, Leslie; Shader, Bryan. Maximum generic nullity of a graph.
  Linear Algebra Appl. 432 (2010), no. 4, 857–866.
• Shader, Bryan; So, Wasin. Skew spectra of oriented graphs.
  Electron. J. Combin. 16 (2009), no. 1, Note 32, 6 pp.
• Kim, In-Jae; Shader, Bryan L. Non-singular acyclic matrices.
  Linear Multilinear Algebra 57 (2009), no. 4, 399–407.
• Kim, I.-J.; Olesky, D. D.; Shader, B. L.; van den Driessche, P.; van der Holst, H.; Vander Meulen, K. N. Generating potentially nilpotent full sign patterns.
• 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. Electron. J. Linear Algebra 18 (2009), 126–145.
• Kim, In-Jae; Shader, Bryan L. Smith normal form and acyclic matrices.
  J. Algebraic Combin. 29 (2009), no. 1, 63–80.
• Berman, Avi; Friedland, Shmuel; Hogben, Leslie; Rothblum, Uriel G.; Shader, Bryan. An upper bound for the minimum rank of a graph.
  Linear Algebra Appl. 429 (2008), no. 7, 1629–1638.
• Kim, In-Jae; Shader, Bryan L. On Fiedler- and Parter-vertices of acyclic matrices.
  Linear Algebra Appl. 428 (2008), no. 11-12, 2601–2613.
• Kim, In-Jae; Shader, Bryan L. Sign patterns that require a positive or nonnegative left inverse.
  Electron. J. Linear Algebra 17 (2008), 209–218.
• Kim, In-Jae; Shader, Bryan L. Classification of trees each of whose associated acyclic matrices with distinct diagonal entries has distinct eigenvalues.
  Bull. Korean Math. Soc. 45 (2008), no. 1, 95–99.
• Berman, Avi; Friedland, Shmuel; Hogben, Leslie; Rothblum, Uriel G.; Shader, Bryan. Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers.
  Electron. J. Combin. 15 (2008), no. 1, Research Paper 25, 19 pp.
• Kim, In-Jae; Olesky, D. D.; Shader, B. L.; van den Driessche, P. Sign patterns that allow a positive or nonnegative left inverse.
  SIAM J. Matrix Anal. Appl. 29 (2007), no. 2, 554–565.
• DeAlba, Luz M.; Hentzel, Irvin R.; Hogben, Leslie; McDonald, Judith; Mikkelson, Rana; Pryporova, Olga; Shader, Bryan; Vander Meulen, Kevin N. Spectrally arbitrary patterns: reducibility and the 2n conjecture for n=5.
  Linear Algebra Appl. 423 (2007), no. 2-3, 262–276.
• de Oliveira, Graciano; Queiró, João Filipe; Shader, Bryan; Zaballa, Ion. Preface to the 11th ILAS Conference Proceedings, Coimbra 2004.
  Held at the University of Coimbra, Coimbra, July 19–22, 2004.
  Linear Algebra Appl. 413 (2006), no. 2-3, 245–246.
• Kirkland, Steve; Shader, Bryan L.; van den Driessche, Pauline. Preface [Directions in Combinatorial Matrix Theory Workshop].
  Held in Banff, AB, May 7–8, 2004. Electron. J. Linear Algebra 14 (2005), 1.
• Olesky, D. D.; Shader, Bryan; van den Driessche, P. Permanents of Hessenberg (0,1)-matrices.
  Electron. J. Combin. 12 (2005), Research Paper 70, 25 pp.
• Cavers, Michael S.; Kim, In Jae; Shader, Bryan L.; Vander Meulen, Kevin N. On determining minimal spectrally arbitrary patterns. Electron. J. Linear Algebra 13 (2005), 240–248.
• Choi, Gyoung-Sik; Hwang, Suk-Geun; Kim, Ik-Pyo; Shader, Bryan L. ($\pm 1$)-invariant sequences and truncated Fibonacci sequences. Linear Algebra Appl. 395 (2005), 303–312.
• Li, Chi-Kwong; Milligan, Thomas; Shader, Bryan L. Non-existence of 5 by 5 full ray-nonsingular matrices. Electron. J. Linear Algebra 11 (2004), 212–240.
• Christian, Justin D.; Shader, Bryan L. Nonexistence results for Hadamard-like matrices.
  Electron. J. Combin. 11 (2004), no. 1, Note 1, 9 pp.
• Cheon, Gi-Sang; Hwang, Suk-Geun; Rim, Seog-Hoon; Shader, Bryan L.; Song, Seok-Zun. Sparse orthogonal matrices. Special issue on the Combinatorial Matrix Theory Conference (Pohang, 2002).
  Linear Algebra Appl. 373 (2003), 211–222.
• Cheon, Gi-Sang; Hwang, Suk-Geun; Shader, Bryan L.; Song, Seok-Zun. Permanents of woven matrices. Linear Algebra Appl. 364 (2003), 223–233.
• Shader, Bryan L.; Suwilo, Saib. Exponents of nonnegative matrix pairs.
  Special issue on nonnegative matrices, M-matrices and their generalizations (Oberwolfach, 2000). Linear Algebra Appl. 363 (2003), 275–293.
• Shader, Bryan L. Set-systems with signed solutions.
  Ninth Conference of the International Linear Algebra Society (Haifa, 2001).
  Linear Algebra Appl. 361 (2003), 121–132.
• Kim, Si-Ju; Shader, Bryan L.; Hwang, Suk-Geun. On matrices with signed null-spaces.
  SIAM J. Matrix Anal. Appl. 24 (2002), no. 2, 570–580.
• Olesky, D. D.; Shader, Bryan; van den Driessche, P. Exponents of tuples of nonnegative matrices.Special issue on algebraic graph theory (Edinburgh, 2001).
  Linear Algebra Appl. 356 (2002), 123–134.
• Kim, Si-Ju; Shader, Bryan L. On matrices which have signed null-spaces.
  Linear Algebra Appl. 353 (2002), 245–255.
• Stuart, Jeffrey L.; Beasley, LeRoy; Shader, Bryan. Irreducible, pattern k-potent ray pattern matrices.Linear Algebra Appl. 346 (2002), 261–271.
• Kim, Si-Ju; Shader, Bryan L. Sign-solvable cone-systems.
  Linear Multilinear Algebra 50 (2002), no. 1, 23–32.
• Kirkland, Stephen J.; Molitierno, Jason J.; Neumann, Michael; Shader, Bryan L. On graphs with equal algebraic and vertex connectivity.
  Special issue dedicated to Professor T. Ando.
  Linear Algebra Appl. 341 (2002), 45–56.
• Eschenbach, Carolyn; Hall, Frank; Hemasinha, Rohan; Kirkland, Stephen; Li, Zhongshan; Shader, Bryan; Stuart, Jeffrey; Weaver, James. Properties of tournaments among well-matched players.
  Amer. Math. Monthly 107 (2000), no. 10, 881–892.
• Boyer, E.; Lister, L.; Shader, B. Sphere-of-influence graphs using the sup-norm.
  Math. Comput. Modelling 32 (2000), no. 10, 1071–1082.
• Kim, Si-Ju; Shader, Bryan L. Linear systems with signed solutions.
  Linear Algebra Appl. 313 (2000), no. 1-3, 21–40.
• Poet, Jeffrey L.; Shader, Bryan L. Score certificate numbers of upset tournaments.
  Discrete Appl. Math. 103 (2000), no. 1-3, 177–189.
• Lee, G. Y.; McDonald, J. J.; Shader, B. L.; Tsatsomeros, M. J. Extremal properties of ray-nonsingular matrices.
  Discrete Math. 216 (2000), no. 1-3, 221–233.
• Cheon, Gi-Sang; Shader, Bryan L. Sparse orthogonal matrices and the Haar wavelet.
  Discrete Appl. Math. 101 (2000), no. 1-3, 63–76.
• Eschenbach, Carolyn; Hall, Frank; Hemasinha, Rohan; Kirkland, Stephen J.; Li, Zhongshan; Shader, Bryan L.; Stuart, Jeffrey L.; Weaver, James R. On almost regular tournament matrices.
  Linear Algebra Appl. 306 (2000), no. 1-3, 103–121.
• Cheon, Gi-Sang; Shader, Bryan L. Sparsity of orthogonal matrices with restrictions.
  Linear Algebra Appl. 306 (2000), no. 1-3, 33–44.
• Molitierno, Jason J.; Neumann, Michael; Shader, Bryan L. Tight bounds on the algebraic connectivity of a balanced binary tree.
  Proceedings of the Eleventh Haifa Matrix Theory Conference (1999).
  Electron. J. Linear Algebra 6 (1999/00), 62–71.
• Gregory, David A.; Watts, Valerie L.; Shader, Bryan L. Biclique decompositions and Hermitian rank. Linear Algebra Appl. 292 (1999), no. 1-3, 267–280.
• Cheon, Gi-Sang; Shader, Bryan L. Constructions for the sparsest orthogonal matrices.
• Cheon, Gi-Sang; Shader, Bryan L. How sparse can a matrix with orthogonal rows be?
  J. Combin. Theory Ser. A 85 (1999), no. 1, 29–40.
• Lee, Gwang-Yeon; Shader, Bryan L. Sign-consistency and solvability of constrained linear systems. Electron. J. Linear Algebra 4 (1998), 1–18.
• Shader, Bryan L. Sign-nonsingular matrices and orthogonal sign-patterns.
  Ars Combin. 48 (1998), 289–296.
• Poet, Jeffrey L.; Shader, Bryan L. Short score certificates for upset tournaments.
  Electron. J. Combin. 5 (1998), Research paper 24, 18 pp.
• Kirkland, Stephen J.; Neumann, Michael; Shader, Bryan L. On a bound on algebraic connectivity: the case of equality.
  Czechoslovak Math. J. 48(123) (1998), no. 1, 65–76.
• Kirkland, Stephen J.; Neumann, Michael; Shader, Bryan L. Bounds on the subdominant eigenvalue involving group inverses with applications to graphs.
  Czechoslovak Math. J. 48(123) (1998), no. 1, 1–20.
• Kirkland, Stephen J.; Neumann, Michael; Shader, Bryan L. Applications of Paz’s inequality to perturbation bounds for Markov chains.
  Linear Algebra Appl. 268 (1998), 183–196.
• Shader, Bryan L. A simple proof of Fiedler’s conjecture concerning orthogonal matrices.
  Rocky Mountain J. Math. 27 (1997), no. 4, 1239–1243.
• Kirkland, Stephen J.; Neumann, Michael; Shader, Bryan L. Distances in weighted trees and group inverse of Laplacian matrices.
  SIAM J. Matrix Anal. Appl. 18 (1997), no. 4, 827–841.
• Adams, Michael J.; Shader, Bryan L. A construction for (t,m,s)-nets in base q.
  SIAM J. Discrete Math. 10 (1997), no. 3, 460–468.
• Shader, Bryan L.; Shader, Chanyoung Lee. Scheduling conflict-free parties for a dating service.
  Amer. Math. Monthly 104 (1997), no. 2, 99–106.
• Gregory, David A.; Vander Meulen, Kevin N.; Shader, Bryan L. Skew rank decompositions.
  Linear Algebra Appl. 244 (1996), 123–154.
• Kirkland, Steve; Neumann, Michael; Shader, Bryan L. Characteristic vertices of weighted trees via Perron values.
  Linear and Multilinear Algebra 40 (1996), no. 4, 311–325.
• Gregory, David A.; Vander Meulen, Kevin N.; Shader, Bryan L. Rank decompositions and signed bigraphs.
  Linear and Multilinear Algebra 40 (1996), no. 4, 283–301.
• Brualdi, Richard A.; Shader, Bryan L. Matrices of sign-solvable linear systems.
  Cambridge Tracts in Mathematics, 116. Cambridge University Press, Cambridge, 1995. {\rm xii}+298 pp. ISBN: 0-521-48296-8
• Shader, Bryan L. Least squares sign-solvability.
  SIAM J. Matrix Anal. Appl. 16 (1995), no. 4, 1056–1073.
• Beasley, LeRoy B.; Kirkland, Stephen J.; Shader, Bryan L. Rank comparisons.
  Linear Algebra Appl. 221 (1995), 171–188.
• Boyer, Elizabeth D.; Shader, Bryan L. On biclique decompositions of complete t-partite graphs.
  Proceedings of a Conference on Graphs and Matrices in honor of John Maybee (Boulder, CO, 1993).
  Linear Algebra Appl. 217 (1995), 31–40.
• Brualdi, Richard A.; Chavey, Keith L.; Shader, Bryan L. Bipartite graphs and inverse sign patterns of strong sign-nonsingular matrices.
  J. Combin. Theory Ser. B 62 (1994), no. 1, 133–150.
• Brualdi, Richard A.; Shader, Bryan L. Minimum permanents on special faces of the polytope of doubly stochastic matrices.
  Linear Algebra Appl. 201 (1994), 103–111.
• Brualdi, Richard A.; Chavey, Keith L.; Shader, Bryan L. Rectangular L-matrices.
  Linear Algebra Appl. 196 (1994), 37–61.
• Kirkland, Stephen J.; Shader, Bryan L. Tournament matrices with extremal spectral properties.
  Linear Algebra Appl. 196 (1994), 1–17.
• Brualdi, Richard A.; Shader, Bryan L. Strong Hall matrices.
  SIAM J. Matrix Anal. Appl. 15 (1994), no. 2, 359–365.
• Brualdi, Richard A.; Shader, Bryan L. Cutsets in bipartite graphs.
  Linear and Multilinear Algebra 34 (1993), no. 1, 51–54.
• Kirkland, Steve; Shader, Bryan L. On multipartite tournament matrices with constant team size.
  Linear and Multilinear Algebra 35 (1993), no. 1, 49–63.
• Beasley, LeRoy B.; Brualdi, Richard A.; Shader, Bryan L. Combinatorial orthogonality.
  Combinatorial and graph-theoretical problems in linear algebra (Minneapolis, MN, 1991),
  207–218, IMA Vol. Math. Appl., 50, Springer, New York, 1993.
• Shader, Bryan L. On biclique partitions of the complete graph.
  Discrete Math. 117 (1993), no. 1-3, 197–213.
• Gregory, D. A.; Kirkland, S. J.; Shader, B. L. Pick’s inequality and tournaments.
  Linear Algebra Appl. 186 (1993), 15–36.
• Shader, Bryan L. Convertible, nearly decomposable, and nearly reducible matrices.
  Linear Algebra Appl. 184 (1993), 37–53.
• Brualdi, Richard A.; Chavey, Keith L.; Shader, Bryan L. Conditional sign-solvability.
  Math. Comput. Modelling 17 (1993), no. 1, 141–148.
• Shader, Bryan L. On tournament matrices.
  Directions in matrix theory (Auburn, AL, 1990).
  Linear Algebra Appl. 162/164 (1992), 335–368.
• Shader, Bryan L. Maximal convertible matrices.
  Proceedings of the Twenty-second Southeastern Conference on Combinatorics, Graph Theory, and Computing (Baton Rouge, LA, 1991).
  Congr. Numer. 81 (1991), 161–172.
• Brualdi, Richard A.; Shader, Bryan L. Matrices of 0’s and 1’s with restricted permanental minors.
  Discrete Math. 96 (1991), no. 3, 161–174.
• Alon, Noga; Brualdi, Richard A.; Shader, Bryan L. Multicolored forests in bipartite decompositions of graphs.
  J. Combin. Theory Ser. B 53 (1991), no. 1, 143–148.
• Brualdi, Richard A.; Shader, Bryan L. On sign-nonsingular matrices and the conversion of the permanent into the determinant.
  Applied geometry and discrete mathematics,
  117–134, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 4, Amer. Math. Soc., Providence, RI, 1991.
• Shader, Bryan Lynn. Biclique partitions and tournaments.
  Thesis (Ph.D.)–The University of Wisconsin – Madison.
  ProQuest LLC, Ann Arbor, MI, 1990. 101 pp.
• Brualdi, Richard A.; Shader, Bryan L. Matrix factorizations of determinants and permanents.
  J. Combin. Theory Ser. A 54 (1990), no. 1, 132–134.
• Katzenberger, G. Shon; Shader, Bryan L. Singular tournament matrices.
  Proceedings of the Twentieth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1989).
  Congr. Numer. 72 (1990), 71–80.