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- W4309285800 abstract "This paper aims at solving the Hermitian SDC problem, i.e., that of textit{simultaneously diagonalizing via $*$-congruence} a collection of finitely many (not need pairwise commute) Hermitian matrices. Theoretically, we provide some equivalent conditions for that such a matrix collection can be simultaneously diagonalized via $^*$-congruence.% by a nonsingular matrix. Interestingly, one of such conditions leads to the existence of a positive definite solution to a semidefinite program (SDP). From practical point of view, we propose an algorithm for numerically solving such problem. The proposed algorithm is a combination of (1) a positive semidefinite program detecting whether the initial Hermitian matrices are simultaneously diagonalizable via $*$-congruence, and (2) a Jacobi-like algorithm for simultaneously diagonalizing via $*$-congruence the commuting normal matrices derived from the previous stage. Illustrating examples by hand/coding in textsc{Matlab} are also presented." @default.
- W4309285800 created "2022-11-25" @default.
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- W4309285800 date "2020-07-28" @default.
- W4309285800 modified "2023-09-26" @default.
- W4309285800 title "Simultaneous diagonalization via congruence of Hermitian matrices: some equivalent conditions and a numerical solution" @default.
- W4309285800 doi "https://doi.org/10.48550/arxiv.2007.14034" @default.
- W4309285800 hasPublicationYear "2020" @default.
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