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On Some Matrix Theoremsof Frobenius and McCoy

Published online by Cambridge University Press:  20 November 2018

J. K. Goldhaber  and
G. Whaples
J. K. Goldhaber
Affiliation:
University of Connecticut
G. Whaples
Affiliation:
Indiana Unwersity
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McCoy, following Frobenius, studied a problem which can be described as follows. Let k be an arbitrary field, kc its algebraic closure, and any algebra of n ⨯ n matrices over k which contains the identity I . Define a canonical ordering to be a set of n mappings λ of , or of a subset of , into kc such that the sequence λ1(A),λ2(A), …, λn(A), for each A ∈ , consists of the characteristic values (roots of det(A — xI) = 0) of A, each with the right multiplicity. Define a canonical ordering to be a Frobenius ordering if, for all non-commutative polynomials f(x1, x2, … , xm) and all finite subsets A1, A2, …, Am of ,

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 332 - 335
Copyright
Copyright © Canadian Mathematical Society 1953

References

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