On the Reduction of a Complex Matrix to Triangular or Diagonal by Consimilarity

摘要

Two n × n complex matrices A and B are said to be consimilar if S?1AS = B for some nonsingular n × n complex matrix S. This paper, by means of real representation of a complex matrix, studies problems of reducing a given n × n complex matrix A to triangular or diagonal form by consimilarity, not only gives necessary and su?cient conditions for contriangularization and condiagonalization of a complex matrix, but also derives an algebraic technique of reducing a matrix to triangular or diagonal form by consimilarity.