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1997•SIAM Journal on Matrix Analysis and ApplicationsRequires access

Determinant of the Sum of a Symmetric and a Skew-Symmetric Matrix

Natália Bebiano, Chi-Kwong Li, João da Providência

Open publisher page 4 citations

Abstract

The set of all possible determinant values of the sum of a (complex) symmetric matrix and a skew-symmetric matrix with prescribed singular values is determined. This set can also be viewed as the best containment region for the determinant of a square matrix X in terms of the singular values of its symmetric and skew-symmetric parts. The technique is extended to study the principal minors of X. Similar problems for real matrices are considered.

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What this paper is about

The set of all possible determinant values of the sum of a (complex) symmetric matrix and a skew-symmetric matrix with prescribed singular values is determined. This set can also be viewed as the best containment region for the determinant of a square matrix X in terms of the singular values of its symmetric and skew-symmetric parts. The technique is extended to study the principal minors of X. Similar problems for real matrices are considered.

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Available abstract

The set of all possible determinant values of the sum of a (complex) symmetric matrix and a skew-symmetric matrix with prescribed singular values is determined. This set can also be viewed as the best containment region for the determinant of a square matrix X in terms of the singular values of its symmetric and skew-symmetric parts. The technique is extended to study the principal minors of X. Similar problems for real matrices are considered.

Key concepts: Mathematics, Skew-symmetric matrix, Symmetric matrix, Symmetric closure, Matrix (chemical analysis), Square matrix, Elementary symmetric polynomial, Combinatorics

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