Spectral inequalities and equalities involving products of matrices (Q5929763)
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scientific article; zbMATH DE number 1586477
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spectral inequalities and equalities involving products of matrices |
scientific article; zbMATH DE number 1586477 |
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Spectral inequalities and equalities involving products of matrices (English)
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12 December 2001
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spectral inequalities
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products of matrices
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inequalities involving eigenvalues
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inequalities involving singular values
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normality
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reducibility
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Inequalities and equalities involving the singular values \(\sigma_1(A),\dots,\sigma_n(A)\), the eigenvalues \(\lambda_1(A),\)NEWLINENEWLINENEWLINE\(\dots,\lambda_n(A)\), and the diagonal entries \(d_1(A),\dots,d_n(A)\) of a matrix \(A\) are studied. The extreme matrices attaining the equalities often have special reducible structure. The results are used to study normality and reducibility of matrices extending the results by \textit{H. F. Miranda} [Linear Algebra Appl. 305, No. 1-3, 151-159 (2000; Zbl 0972.15008)]. Extension of the results to more than two matrices is discussed.
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