Previous |  Up |  Next


inertia; sign pattern matrix; tridiagonal matrix
A matrix whose entries consist of elements from the set $\lbrace +,-,0\rbrace $ is a sign pattern matrix. Using a linear algebra theoretical approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign matrices.
[1] B. E. Cain and E. Marques de Sá: The inertia of Hermitian matrices with a prescribed $2\times 2$ block decomposition. Linear and Multilinear Algebra 31 (1992), 119–130. DOI 10.1080/03081089208818128 | MR 1199047
[2] B. E. Cain and E. Marques de Sá: The inertia of certain skew-triangular block matrices. Linear Algebra Appl. 160 (1992), 75–85. MR 1137844
[3] C. Eschenbach and C. R. Johnson: A combinatorial converse to the Perron-Frobenius theorem. Linear Algebra Appl. 136 (1990), 173–180. MR 1061544
[4] C. Eschenbach and C. R. Johnson: Sign patterns that require real, nonreal or pure imaginary eigenvalues. Linear and Multilinear Algebra 29 (1991), 299–311. DOI 10.1080/03081089108818079 | MR 1119461
[5] Y. Gao and Y. Shao: The inertia set of nonnegative symmetric sign pattern with zero diagonal. Czechoslovak Math. J. 53 (2003), 925–934. DOI 10.1023/B:CMAJ.0000024531.10708.9f | MR 2018840
[6] F. J. Hall and Z. Li: Inertia sets of symmetric sign pattern matrices. Numer. Math. J. Chinese Univ. (English Ser.) 10 (2001), 226–240. MR 1884971
[7] F. J. Hall, Z. Li and Di Wang: Symmetric sign pattern matrices that require unique inertia. Linear Algebra Appl. 338 (2001), 153–169. MR 1861120
[8] R. A. Horn and C. R. Johnson: Matrix Analysis, Cambridge University Press, Cambridge. 1985. MR 0832183
[9] C. Jeffries and C. R. Johnson: Some sign patterns that preclude matrix stability. SIAM J. Matrix Anal. Appl. 9 (1988), 19–25. MR 0938055
Partner of
EuDML logo