On the Inertia of Intervals of Matrices

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 1990 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Matrix Analysis and Applications, volume 11, pages 565-574 (issn: 0895-4798, eissn: 1095-7162,

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Authors: Daniel Hershkowitz; Hans Schneider;

doi: 10.1137/0611040

On the Inertia of Intervals of Matrices

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Abstract

The inertia of intervals and lines of matrices is investigated. For complex $n \times n$ matrices A and B it is shown that, under mild nonsingularity conditions, $A + tB$ changes inertia at no more than $n^2 $ real values of t. Conditions are given for the constancy of the inertia of $A + tB$, where t lies in a real interval. These conditions generalize and organize some known results.

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