Root spreads for polynomials and Hermitian matrix pencils (Q1893099)
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scientific article; zbMATH DE number 769037
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Root spreads for polynomials and Hermitian matrix pencils |
scientific article; zbMATH DE number 769037 |
Statements
Root spreads for polynomials and Hermitian matrix pencils (English)
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15 November 1995
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Let \(f(x)\) be a polynomial with real roots \(x_ 1,\dots,x_ n\) and let be \(f_ i(x)\), \(i= 1,\dots, n\) be certain linear combinations of the polynomials \(f(x)/(x- x_ i)\). The spread of a polynomial is the difference of its largest and smallest root. The author compare the spreads of \(f(x)\) and of the \(f_ i(x)\). This is applied to the spreads of the eigenvalues of an Hermitian matrix and the spreads of its principal submatrices.
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root spreads for polynomials
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Hermitian matrix pencils
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spreads of the eigenvalues
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Hermitian matrix
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