On the similarity of matrices AB and BA over a field
Journal Title: Карпатські математичні публікації - Year 2018, Vol 10, Issue 2
Abstract
Let A and B be n-by-n matrices over a field. The study of the relationship between the products of matrices AB and BA has a long history. It is well-known that AB and BA have equal characteristic polynomials (and, therefore, eigenvalues, traces, etc.). One beautiful result was obtained by H. Flanders in 1951. He determined the relationship between the elementary divisors of AB and BA, which can be seen as a criterion when two matrices C and D can be realized as C=AB and D=BA. If one of the matrices (A or B) is invertible, then the matrices AB and BA are similar. If both A and B are singular then matrices AB and BA are not always similar. We give conditions under which matrices AB and BA are similar. The rank of matrices plays an important role in this investigation.
Authors and Affiliations
V. M. Prokip
Keywords
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- EP ID EP535496
- DOI 10.15330/cmp.10.2.352-359
- Views 87
- Downloads 0
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