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A note on the matrix equationXA – AX = Xp

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
424
Identifiers
DOI: 10.1016/j.laa.2007.02.008
Keywords
  • Matrix Equation
  • Lie Algebra
  • Shemesh Theorem
Disciplines
  • Mathematics

Abstract

Abstract Another, more elementary proof is given of Proposition 2.3 in a recent paper by Dietrich Burde. This proposition says that n × n matrices A and X over an algebraically closed field K of characteristic zero satisfying the equality in the title of this paper can be simultaneously triangularized. The proposed proof is based on the Shemesh criterion for two matrices to have a common eigenvector.

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