The \(\phi_J \) polar decomposition of matrices with rank 2 (Q959881)
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scientific article; zbMATH DE number 5382415
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \(\phi_J \) polar decomposition of matrices with rank 2 |
scientific article; zbMATH DE number 5382415 |
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The \(\phi_J \) polar decomposition of matrices with rank 2 (English)
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12 December 2008
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As is well known that if a matrix has a \(\phi_J\) polar decomposition, then it is of even rank. This paper provides necessary and sufficient conditions for a \(2n\)-by-\(2n\) matrix of rank 2 to have a \(\phi_J\) polar decomposition. The main result is proved by reducing an arbitrary matrix via symplectic row and column operations into matrices of simpler forms.
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\(\phi_J\) polar decomposition
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symplectic matrices
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symplectic equivalence
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reduction
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rank
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