Similarity and matrices of constant rank (Q1124924)
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scientific article; zbMATH DE number 1371412
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Similarity and matrices of constant rank |
scientific article; zbMATH DE number 1371412 |
Statements
Similarity and matrices of constant rank (English)
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29 November 1999
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If \(M\) and \(N\) are in \(M(n,\mathbb{C})\) and have the same rank, then there exist \(P\) and \(Q\) in \(GL(n,\mathbb{C})\) such that \(PMQ=N\). It is shown that \(P\) and \(Q\) can be chosen to be similar, or, equivalently, that there exist invertible matrices \(R\) and \(S\) such that \(RSMSR=N\).
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similarity
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matrices of constant rank
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permutation matrix
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