On the Reduction of a Matrix to Triangular or Diagonal Form by Consimilarity
Copyright policy )On the Reduction of a Matrix to Triangular or Diagonal Form by Consimilarity
The authors consider the transformation \(A\to SA\bar S^{-1}\) where S is nonsingular. They give a motivation for such an equivalence relation and then study the extent to which a diagonal or triangular canonical form can be obtained. This leads to natural analogs of spectral theory both for general S and for unitary S. There is an application to the simultaneous reduction of a family of matrices under this transformation.
diagonal form, Eigenvalues, singular values, and eigenvectors, canonical form, Canonical forms, reductions, classification, consimilarity, triangular form, Factorization of matrices, simultaneous reduction
diagonal form, Eigenvalues, singular values, and eigenvectors, canonical form, Canonical forms, reductions, classification, consimilarity, triangular form, Factorization of matrices, simultaneous reduction
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