Closest matrices in the space of generalized doubly stochastic matrices (Q1270897)
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scientific article; zbMATH DE number 1218618
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Closest matrices in the space of generalized doubly stochastic matrices |
scientific article; zbMATH DE number 1218618 |
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Closest matrices in the space of generalized doubly stochastic matrices (English)
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4 May 1999
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The author constructs the closest matrix \(B^*\) in \(\Omega_n\) (the collection of doubly stochastic \(n\times n\) real matrices) to a given real matrix \(A\) in \(M_n\) (the space of all \(n\times n\) real matrices). He also proves that \(B^* =(I_n-J_n) A(J_n-J_n) +J_n\), where \(J_n\) is \(n\times n\) real matrix the entries of which are all equal to \(1/n\) and \(I_n\) is \(n\times n\) real identity matrix in \(M_n\).
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doubly stochastic matrices
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closest matrix
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