Perturbation Bounds for Determinants and Characteristic Polynomials

Perturbation Bounds for Determinants and Characteristic Polynomials

We derive absolute perturbation bounds for the coefficients of the characteristic polynomial of a $n\times n$ complex matrix. The bounds consist of elementary symmetric functions of singular values, and suggest that coefficients of normal matrices are better conditioned with regard to absolute pertu...

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Veröffentlicht in:SIAM journal on matrix analysis and applications 2008-01, Vol.30 (2), p.762-776
Hauptverfasser: Ipsen, Ilse C. F., Rehman, Rizwana
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Eigenvalues
Matrix
Polynomials
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Rehman, Rizwana
description We derive absolute perturbation bounds for the coefficients of the characteristic polynomial of a $n\times n$ complex matrix. The bounds consist of elementary symmetric functions of singular values, and suggest that coefficients of normal matrices are better conditioned with regard to absolute perturbations than those of general matrices. When the matrix is Hermitian positive-definite, the bounds can be expressed in terms of the coefficients themselves. We also improve absolute and relative perturbation bounds for determinants. The basis for all bounds is an expansion of the determinant of a perturbed diagonal matrix.
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subjects Eigenvalues
Matrix
Polynomials
title Perturbation Bounds for Determinants and Characteristic Polynomials
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