Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599602 | Linear Algebra and its Applications | 2014 | 26 Pages |
Abstract
It is shown that for any kâ{1,2,â¦,(mâ1)!} there exist m invertible complex matrices such that among the m! products AÏ=AÏ(1)AÏ(2)â¯AÏ(m), ÏâSm, exactly k different similarity classes occur. The cases in which the matrices Ai are upper triangular or are 2-by-2 are considered in detail. In the former case, it is shown that any mâ1 unispectral matrices with common eigenvalue may be found among the AÏ, and in the latter case it is shown explicitly how to achieve (mâ1)! and (mâ1)!2 similarity classes, as well as any number from 1 to 6 when m=4. Other particular results are given, as well as a discussion of further natural questions.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Susana Furtado, Charles R. Johnson,