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Proceedings of the American Mathematical Society

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

 

 

On the characteristic roots of real matrices


Author: H. H. Schaefer
Journal: Proc. Amer. Math. Soc. 28 (1971), 91-92
MSC: Primary 15.25
MathSciNet review: 0271126
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Abstract: If $ A$ is a real $ n \times n$-matrix whose absolute $ \vert A\vert$ has spectral radius 1, and if $ \varepsilon $ is a unimodular characteristic value of $ A$, then all odd (respectively, even) powers of $ \varepsilon $ are characteristic values of $ A$ (respectively, of $ \vert A\vert$). In particular, such $ \varepsilon $ must be a $ k$th root of unity for some $ k, 1 \leqq k \leqq 2n$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0271126-2
Keywords: $ n \times n$-matrix, characteristic value, unimodular spectrum
Article copyright: © Copyright 1971 American Mathematical Society