Stabilization by a diagonal matrix
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- by C. S. Ballantine
- Proc. Amer. Math. Soc. 25 (1970), 728-734
- DOI: https://doi.org/10.1090/S0002-9939-1970-0260765-X
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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.References
- Ky Fan, Topological proofs for certain theorems on matrices with non-negative elements, Monatsh. Math. 62 (1958), 219–237. MR 95856, DOI 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
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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