On extremum properties of orthogonal quotients matrices (Q847212)
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scientific article; zbMATH DE number 5669177
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On extremum properties of orthogonal quotients matrices |
scientific article; zbMATH DE number 5669177 |
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On extremum properties of orthogonal quotients matrices (English)
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12 February 2010
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The extremum properties of orthogonal quotients matrices are investigated. The orthogonal quotients equality that is proved expresses the Frobenius norm of a difference between two matrices as a difference between the norms of two matrices, turning the Eckart-Young minimum norm problem into an equivalent maximum norm problem. The symmetric version of this equality involves traces of matrices and adds new insight into Ky Fan's extremum problems. By the comparison of the two cases, an important similarity between the Eckart-Young theorem and Ky Fan's maximum principle arises. For orthogonal quotients matrices, 'rectangular' extensions of Ky Fan's extremum principles are derived, that consider maximizing (or minimizing) sums of powers of singular values.
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eigenvalues
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singular values
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Rayleigh quotient
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orthogonal quotient matrices
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the orthogonal quotients equality
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Eckart-Young theorem
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Ky Fan's extremum principles
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Frobenius norm
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