On the Unitary Similarity of Matrices |
Common terms and phrases
A₂ automorphs B₁ block diagonal Brenner C₁ canonical matrix canonical set characteristic vector space column vectors columns form complex field Corollary 1-3 corresponding D₁ decomposable diag diagonal blocks diagonal elements diagonal matrix diagonal unitary group dimension direct sum distinct characteristic roots easily seen elements of G equation exists a unitary F₁ form a normal G₁ gonal group G hence Hermitian matrices identity matrix implies integer invariant under G K₂ Lemma linearly independent M₁ M₂ Moreover n x k n x n matrices N₂ non-singular matrix normal matrices normal unitary basis null matrix obtain ordered set ordering relation orthogonal P₁ pairs permutation matrix polar form polynomial in normal positive definite Hermitian properties R-ordered rational canonical form representation F S₁ S₂ scalar Specht square matrix sub-group of G sub-matrices Theorem 4-1 triangular U₁ uniquely determined unitarily similar unitary matrix unitary transform V₁ W₁