The \(\psi_S\) polar decomposition (Q837004)
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scientific article; zbMATH DE number 5602608
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \(\psi_S\) polar decomposition |
scientific article; zbMATH DE number 5602608 |
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The \(\psi_S\) polar decomposition (English)
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10 September 2009
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Let \(S\) be a nonsingular \(n\) by \(n\) complex matrix. The authors define \(\psi_S(A)\) for \(A\) being nonsingular and singular, respectively. It is proved that every nonsingular \(A\) has a \(\psi_S\) polar decomposition \(A=RE\), where \(R\) is \(\psi_S\) orthogonal and \(E\) is \(\psi_S\) symmetric. The authors also determine which singular matrices have a \(\psi_S\) polar decomposition.
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\(\psi_S\) polar decomposition
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\(\psi_S\) orthogonal matrices
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\(\psi_S\) symmetric matrices
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\(\psi_S\) antiorthogonal matrices
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coninvolutory matrices
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skew-coninvolutory matrices
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