Stabilization by a diagonal matrix-Reference-Cited by-同舟云学术

Stabilization by a diagonal matrix

Published:1970 Issue:4 Volume:25 Page:728-734
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Ballantine C. S.

Abstract

In this paper it is shown that, given a complex square matrix A A all of whose leading principal minors are nonzero, there is a diagonal matrix D D such that the product D A DA of the two matrices has all its characteristic roots positive and simple. This result is already known for real A A , but two new proofs for this case are given here.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1970-025-04/S0002-9939-1970-0260765-X/S0002-9939-1970-0260765-X.pdf

Reference2 articles.

1. Topological proofs for certain theorems on matrices with non-negative elements;Fan, Ky;Monatsh. Math.,1958

2. On the stabilization of matrices and the convergence of linear iterative processes;Fisher, Michael E.;Proc. Cambridge Philos. Soc.,1958

Cited by 38 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Stability of ecological systems: A theoretical review;Physics Reports;2024-10

2. Sufficient Conditions for Linear Stability of Complex-Balanced Equilibria in Generalized Mass-Action Systems;SIAM Journal on Applied Dynamical Systems;2024-01-22

3. Zero-nonzero tree patterns that allow;Linear and Multilinear Algebra;2021-10-12

4. Formation Tracking of Nonholonomic Systems on the Special Euclidean Group under Fixed and Switching Topologies: An Affine Formation Strategy;SIAM Journal on Control and Optimization;2021-01

5. Matrix Positivity;CAMB TRACT MATH;2020-08-31