A criterion for unitary similarity of upper triangular matrices in general position

Author(s)

Farenick, Douglas ^[1] ; Futorny, Vyacheslav ^[2] ; Gerasimova, Tatiana G. ^[3] ; Sergeichuk, Vladimir V. ^[4] ; Shvai, Nadya ^[3]

Affiliation

^[1] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2 - Canada

^[2] Univ Sao Paulo, Dept Math, Sao Paulo - Brazil

^[3] Kiev Natl Taras Shevchenko Univ, Fac Mech & Math, Kiev - Ukraine

^[4] Ukrainian Acad Sci, Inst Math, Kiev - Ukraine

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 435, n. 6, p. 1356-1369, SEP 15 2011.
• Web of Science Citations: 3

Abstract

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = {[}a(ij)] and B = {[}b(ij)] be upper triangular n x n matrices that are not similar to direct sums of square matrices of smaller sizes, or are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if parallel to h(A(k))parallel to = parallel to h(B(k))parallel to for all h is an element of C vertical bar x vertical bar and k = 1, ..., n, where A(k) := {[}a(ij)](i.j=1)(k) and B(k) := {[}b(ij)](i.j=1)(k) are the leading principal k x k submatrices of A and B, and parallel to . parallel to is the Frobenius norm. (C) 2011 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 10/07278-6 - Canonical matrices and their miniversal deformations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Grants - Visiting Researcher Grant - International