On the multiplicative inverse eigenvalue problem (Q1078633)
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scientific article; zbMATH DE number 3961847
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the multiplicative inverse eigenvalue problem |
scientific article; zbMATH DE number 3961847 |
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On the multiplicative inverse eigenvalue problem (English)
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1986
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A result obtained by \textit{S. Friedland} [ibid. 17, 15-51 (1977; Zbl 0358.15007)] for complex matrices is extended to matrices over an algebraically closed field K. Let A be an n-square matrix over K with nonzero principal minors, and let \(w_ 1,...,w_ n\) be elements of K. The author shows that there exists a diagonal matrix D for which DA has eigenvalues \(w_ 1,...,w_ n\); moreover, the number of such matrices D is finite and does not exceed n !.
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multiplicative inverse eigenvalue problem
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matrices over an algebraically closed field
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