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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
DOI: https://doi.org/10.1090/S0002-9939-1971-0271126-2
MathSciNet review: 0271126
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Abstract: If $A$ is a real $n \times n$-matrix whose absolute $|A|$ 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 $|A|$). In particular, such $\varepsilon$ must be a $k$th root of unity for some $k, 1 \leqq k \leqq 2n$.


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Keywords: <!– MATH $n \times n$ –> <IMG WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$n \times n$">-matrix, characteristic value, unimodular spectrum
Article copyright: © Copyright 1971 American Mathematical Society