The canonical Schur form of a unitarily quasidiagonalizable matrix (Q1569267)

The geometrical and computational interpretation of the nonzero off-diagonal element of the canonical Schur form are given. For the class of unitary quasidiagonalizable matrices, a unique Schur form is singled out in the set of all Schur forms. This particular form can be considered as the canonical one. The quasidiagonalizability as a property of a matrix \(A\) is shown to admit a characterization in terms of a finite set of equations in \(A\) and \(A^{\star}\). It is proven that the class of quasidiagonalizable matrices contains all matrices with quadratic minimal polynomials.