Every invertible matrix is diagonally equivalent to a matrix with distinct eigenvalues (Q417518)
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scientific article; zbMATH DE number 6034494
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Every invertible matrix is diagonally equivalent to a matrix with distinct eigenvalues |
scientific article; zbMATH DE number 6034494 |
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Every invertible matrix is diagonally equivalent to a matrix with distinct eigenvalues (English)
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14 May 2012
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diagonal equivalence
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diagonal matrix
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distinct eigenvalues
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Gershgorin's circle theorem
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The authors prove the following result: For every invertible complex \(n\times n\)-matrix \(A\), there exists a diagonal matrix \(D\) such that \(AD\) has \(n\) distinct eigenvalues.NEWLINENEWLINEThe result follows from an application of Gershgorin's circle theorem.
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