The Jordan forms of AB and BA∗
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The relationship between the Jordan forms of the matrix products AB and BA for
some given A and B was first described by Harley Flanders in 1951. Their non-zero eigenvalues and
non-singular Jordan structures are the same, but their singular Jordan block sizes can differ by 1.
We present an elementary proof that owes its simplicity to a novel use of the Weyr characteristic.
Date issued
2009-06Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Electronic Journal of Linear Algebra
Publisher
International Linear Algebra Society
Citation
Lippert, Ross A. and Gilbert Strang. "The Jordan Forms of AB and BA*." Electronic Journal of Linear Algebra 18 (2009) : 281-288.
Version: Final published version
ISSN
1081-3810