Arveson's criterion for unitary similarity

This paper is an exposition of W.B. Arveson's complete invariant for the unitary similarity of complex, irreducible matrices.Comment: To appear in Linear Algebra and its Application

Criterion of unitary similarity for upper triangular matrices in general position

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A and B be upper triangular n-by-n matrices that (i) are not similar to direct sums of matrices of smaller sizes, or (ii) are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if ||h(A_k)||=||h(B_k)|| for all complex polynomials h(x) and k=1, 2, . . , n, where A_k and B_k are the principal k-by-k submatrices of A and B, and ||M|| is the Frobenius norm of M.Comment: 16 page

A complete unitary similarity invariant for unicellular matrices

We present necessary and sufficient conditions for an n\times n complex matrix B to be unitarily similar to a fixed unicellular (i.e., indecomposable by similarity) n\times n complex matrix AComment: 16 page