Stability and convex hulls of matrix powers |
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Authors: | Patrick K. Torres |
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Affiliation: | Department of Mathematics and Statistics, Washington State University, Pullman, WA, USA. |
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Abstract: | Invertibility of all convex combinations of A and I is equivalent to the real eigenvalues of A, if any, being positive. Invertibility of all matrices whose rows are convex combinations of the respective rows of A and I is equivalent to A having positive principal minors (i.e. being a P-matrix). These results are extended by considering convex combinations of higher powers of A and of their rows. The invertibility of matrices in these convex hulls is associated with the eigenvalues of A lying in open sectors of the right-half plane and provides a general context for the theory of matrices with P-matrix powers. |
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Keywords: | P-matrix nonsingularity positive stability matrix powers matrix hull |
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