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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Stabilization by a diagonal matrix


Author: C. S. Ballantine
Journal: Proc. Amer. Math. Soc. 25 (1970), 728-734
MSC: Primary 15.25
DOI: https://doi.org/10.1090/S0002-9939-1970-0260765-X
MathSciNet review: 0260765
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Abstract: In this paper it is shown that, given a complex square matrix $ A$ all of whose leading principal minors are nonzero, there is a diagonal matrix $ D$ such that the product $ DA$ of the two matrices has all its characteristic roots positive and simple. This result is already known for real $ A$, but two new proofs for this case are given here.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0260765-X
Keywords: Diagonal matrix, stable matrix, leading principal minors, characteristic roots, positive simple roots, continuity of roots, separation of roots, parallelotope, continuous mapping
Article copyright: © Copyright 1970 American Mathematical Society