On the Reduction of a Matrix to Triangular or Diagonal Form by Consimilarity
Yoo Pyo Hong, Roger A. Horn · SIAM Journal on Algebraic and Discrete Methods · 1986
We study the problem of reducing a given n-by-n complex matrix A to triangular or diagonal form by a transformation of the form $A \to SA\bar S^{ - 1} $, where S is a nonsingular n-by-n complex matrix. We also consider the special case of this reduction in which S is unitary, and a generalization to the problem of simultaneously reducing a family of matrices in this way. Natural analogues of eigenvalues and eigenvectors arise in this context; they have both familiar and unfamiliar properties.