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 | References | Similar Articles | Additional Information
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.
- Ky Fan, Topological proofs for certain theorems on matrices with non-negative elements, Monatsh. Math. 62 (1958), 219–237. MR 95856, DOI https://doi.org/10.1007/BF01303967
- Michael E. Fisher and A. T. Fuller, On the stabilization of matrices and the convergence of linear iterative processes, Proc. Cambridge Philos. Soc. 54 (1958), 417–425. MR 95584
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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