Comparison of infinity norms of matrix inverses (Q1109851)
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scientific article; zbMATH DE number 4071115
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Comparison of infinity norms of matrix inverses |
scientific article; zbMATH DE number 4071115 |
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Comparison of infinity norms of matrix inverses (English)
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1987
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The author studies matrices for which addition of positive numbers to the diagonal cause nonincreasing changes in the \(\ell_{\infty}\) norm of rows of its inverse. He proves that if T is a matrix having an inverse with positive diagonal and no zero off diagonal entries then \(T=D^{- 1}SD\), where D is a diagonal matrix with the diagonal entries \(+1\) or -1 and S has a positive inverse. Another result concerns matrices with a nonnegative diagonal of the inverse.
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infinity norm
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matrix inverse
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positive diagonal
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diagonal matrix
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positive inverse
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