The matrix equation \(\log (XY)=\log (X)+\log (Y)\) (Q848568)
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scientific article; zbMATH DE number 5677353
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The matrix equation \(\log (XY)=\log (X)+\log (Y)\) |
scientific article; zbMATH DE number 5677353 |
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The matrix equation \(\log (XY)=\log (X)+\log (Y)\) (English)
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4 March 2010
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Let \(X,Y\) be \(n\times n\) complex matrices such that \(X,Y,XY\) have no eigenvalues on \(\mathbb R^-\) and \(\log (XY)=\log (X)+\log (Y)\). The authors prove that if \(n=2\), or if \(n\geqslant 3\) and \(X,Y\) are simultaneously triangularizable, then \(X,Y\) commute. In both cases the problem is reduced to a result in complex analysis.
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matricial logarithm
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complex analysis
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