Holtz, Olga; Schneider, Hans Open problems on GKK \(\tau\)-matrices. (English) Zbl 1160.15305 Linear Algebra Appl. 345, No. 1-3, 263-267 (2002). Summary: We propose several open problems on GKK \(\tau\)-matrices raised by examples showing that some such matrices are unstable. Cited in 20 Documents MSC: 15A15 Determinants, permanents, traces, other special matrix functions 15A18 Eigenvalues, singular values, and eigenvectors 15A29 Inverse problems in linear algebra 15B57 Hermitian, skew-Hermitian, and related matrices Keywords:P-matrices; M-matrices; Stability; Eigenvaluemonotonicity; Principalminors; Almost principal minors; Dispersal; Hadamard–Fischer inequality; Newton inequality; Inverse eigenvalue problem PDFBibTeX XMLCite \textit{O. Holtz} and \textit{H. Schneider}, Linear Algebra Appl. 345, No. 1--3, 263--267 (2002; Zbl 1160.15305) Full Text: DOI arXiv Link References: [1] Biegler-König, F. W., Construction of band matrices from spectral data, Linear Algebra Appl., 40, 79-87 (1981) · Zbl 0468.15006 [2] Carlson, D., Weakly sign-symmetric matrices and some determinantal inequalities, Colloq. Math., 17, 123-129 (1967) · Zbl 0147.27502 [3] Carlson, D., A class of positive stable matrices, J. Res. Nat. Bur. Standards B, 78, 1-2 (1974) · Zbl 0281.15020 [4] N.G. Čebotarev, N.N. Meı̆man, The Routh-Hurwitz problem for polynomials and entire functions. Real Quasipolynomials with \(r=3,\); N.G. Čebotarev, N.N. Meı̆man, The Routh-Hurwitz problem for polynomials and entire functions. Real Quasipolynomials with \(r=3,\) [5] Engel, G. M.; Schneider, H., The Hadamard-Fischer inequality for a class of matrices defined by eigenvalue monotonicity, Linear and Multilinear Algebra, 4, 155-176 (1976) [6] Fan, K., Subadditive functions on a distributive lattice and an extension of Szász’s inequality, J. Math. Anal. Appl., 18, 262-268 (1967) · Zbl 0204.02701 [7] Gantmacher, F. R.; Krein, M. G., Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems (1950), Gostechizdat · Zbl 0041.35502 [8] Hershkowitz, D., Recent directions in matrix stability, Linear Algebra Appl., 171, 161-186 (1992) · Zbl 0759.15010 [9] Hershkowitz, D.; Berman, A., Notes on \(ω\)- and \(τ\)-matrices, Linear Algebra Appl., 58, 169-183 (1984) · Zbl 0543.15014 [10] Kotelyansky (Koteljanskii), D. M., A property of sign-symmetric matrices, Uspekhi Mat. Nauk. (NS), 8, 163-167 (1952), also Amer. Math. Soc. Transl. Ser. 2, 27 (1963) 19-23 [11] Holtz, O., Not all GKK \(τ\)-matrices are stable, Linear Algebra Appl., 291, 235-244 (1999) · Zbl 0968.15014 [12] Mehrmann, V., On some conjectures on the spectra of \(τ\)-matrices, Linear and Multilinear Algebra, 16, 101-112 (1984) · Zbl 0574.15007 [13] C. Niculescu, A new look at Newton’s inequalities, J. Inequal. Pure Appl. Math. 1 (2) (2000); C. Niculescu, A new look at Newton’s inequalities, J. Inequal. Pure Appl. Math. 1 (2) (2000) · Zbl 0972.26010 [14] Varga, R., Recent results in linear algebra and its applications, (in Numerical Methods in: Linear Algebra, Proceedings of the Third Seminar of Numerical Applied Mathematics. in Numerical Methods in: Linear Algebra, Proceedings of the Third Seminar of Numerical Applied Mathematics, Akad. Nauk. SSSR Sibirsk, Otdel. Vychisl. Tsentr. Novosibirsk (1978)), 5-15 · Zbl 0435.15002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.