The Homomorphic Mapping of Certain Matric Algebras onto Rings of Diagonal Matrices
- 1 January 1952
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 4, 31-42
- https://doi.org/10.4153/cjm-1952-003-0
Abstract
The problem of determining the conditions under which a finite set of matrices A1A2, … , Ak has the property that their characteristic roots λ1j, λ2j, … , λki (j = 1, 2, …, n) may be so ordered that every polynomial f(A1A2 … , Ak) in these matrices has characteristic roots f(λ1j, λ2j …,λki) (j = 1, 2, … , n) was first considered by Frobenius [4]. He showed that a sufficient condition for the (Ai〉 to have this property is that they be commutative. It may be shown by an example that this condition is not necessary.J. Williamson [9] considered this problem for two matrices under the restriction that one of them be non-derogatory. He then showed that a necessary and sufficient condition that these two matrices have the above property is that they satisfy a certain finite set of matric equations.Keywords
This publication has 3 references indexed in Scilit:
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- On the characteristic roots of matric polynomialsBulletin of the American Mathematical Society, 1936
- The Simultaneous Reduction of Two Matrices to Triangle FormAmerican Journal of Mathematics, 1935