Some Results of Sign patterns Allowing Simultaneous Unitary Diagonalizability

Authors: Xin-Lei Feng, Ting-Zhu Huang

Abstract:

Allowing diagonalizability of sign pattern is still an open problem. In this paper, we make a carefully discussion about allowing unitary diagonalizability of two sign pattern. Some sufficient and necessary conditions of allowing unitary diagonalizability are also obtained.

Keywords: Sign pattern, unitary diagonalizability, eigenvalue, allowing diagonalizability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331665

References:

[1] Y.L. Shao, Y. B. Gao, Sign patterns that allow diagonalizability, Linear Algebra Appl., 359(1-3)(2003): 113-119.
[2] M.I. Bueno, S. Furtado, C.R. Johnson, Congruence of Hermitian matrices by Hermitian matrices, Linear Algebra Appl, 425(1)(2007), 63-76.
[3] C.A. Echenbach, C.R. Johnson, Sign patterns that require repeated eigenvalues, Linear Algebra Appl., 190 (1993): 169-179.
[4] R.A. Brualdi, H.J. Ryser, Combinatorial Matrix Theory, Cambridge University Press, Cambridge, 1991.
[5] R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.