Inequalities of Rayleigh quotients and bounds on the spectral radius of nonnegative symmetric matrices (Q1368768)
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scientific article; zbMATH DE number 1067951
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inequalities of Rayleigh quotients and bounds on the spectral radius of nonnegative symmetric matrices |
scientific article; zbMATH DE number 1067951 |
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Inequalities of Rayleigh quotients and bounds on the spectral radius of nonnegative symmetric matrices (English)
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23 April 1998
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Let \(A\) be a nonnegative symmetric matrix, \(u\) be a nonnegative vector. \(Q_A(u)= u^TAu/ u^Tu\) is called the Rayleigh quotient of \(u\) under \(A\). The following result is obtained: \(Q_A (\sqrt{u\circ Au})\leq Q_A(u)\), where \(\sqrt{\;}\) denotes coordinatewise square roots and \(\circ\) is the Hadamard product. \(Q_A(Au)\) may be smaller than \(Q_A(u)\).
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inequalities
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bounds
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spectral radius
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nonnegative symmetric matrix
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Rayleigh quotient
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Hadamard product
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