A relationship between characteristic values and vectors
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- by E. T. Beasley and P. M. Gibson PDF
- Proc. Amer. Math. Soc. 43 (1974), 71-78 Request permission
Abstract:
It is shown that for all nonzero $n$-component column vectors $\alpha$ and $\beta$ over a field $F$ there exists a set $\Gamma$ of $n$-square matrices over $F$ of cardinality ${n^2} - 2n + 2$ such that, for each $n$-square matrix $A$ over $F,A\alpha = \alpha$ or ${A^T}\beta = \beta$ if and only if 1 is a characteristic value of PA for every $P \in \Gamma$.References
- Richard A. Brualdi and Helmut W. Wielandt, A spectral characterization of stochastic matrices, Linear Algebra Appl. 1 (1968), no. 1, 65–71. MR 223387, DOI 10.1016/0024-3795(68)90049-9
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 71-78
- MSC: Primary 15A18
- DOI: https://doi.org/10.1090/S0002-9939-1974-0340274-3
- MathSciNet review: 0340274