Decomposition of generalized polynomial symmetric matrices. (Q1415287)
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scientific article; zbMATH DE number 2012698
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Decomposition of generalized polynomial symmetric matrices. |
scientific article; zbMATH DE number 2012698 |
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Decomposition of generalized polynomial symmetric matrices. (English)
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3 December 2003
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A complete description of nonnegative square matrices satisfying the equation \[ (A^p)^T= \sum^t_{i=1} \alpha_i A^{m_i}, \] where \(p< m_1< m_2<\cdots< m_t\) are positive integers and all \(\alpha_i\) are positive is given. Some applications to stochastic and \(\{0,1\}\) matrices are presented. An interesting application to the directed graph representing flights is given.
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nonnegative matrices
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group inverse
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Drazin pseudoinverse
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stochastic matrices
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\(\{0,1\}\) matrices
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matrix equation
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