Equivalent conditions for simultaneous diagonalization via ^*-congruence of Hermitian matrices
share
This paper aims at giving some equivalent conditions for that a collection of finitely many of Hermitian matrices can be simultaneously diagonalizable via congruence (SDC) by a nonsingular matrix. It surprisingly turns out that one of such equivalent conditions applies the semidefinite programming (SDP), which leads to a practical usefulness. As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in [J-B. Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization, SIAM Review 49(2), 2007]. Corresponding algorithms and illustrating examples by hand/coding are also presented.
READ FULL TEXT
