A criterion for unitary similarity of upper triangular matrices in general position
Copyright policy )A criterion for unitary similarity of 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.
16 pages
- UNIVERSIDADE DE SAO PAULO Brazil
- University of Sao Paulo Brazil
- University of Regina Canada
- National Academy of Sciences of Ukraine Ukraine
- University of Sao Paulo Brazil
unitary similarity, Numerical Analysis, Algebra and Number Theory, Canonical forms, reductions, classification, Unitary similarity, 15A21, Frobenius norm, Classification, general position of matrices, 15A21, 15A60, General position, classification of matrices, 15A60, FOS: Mathematics, Discrete Mathematics and Combinatorics, triangular matrices, Geometry and Topology, Representation Theory (math.RT), Mathematics - Representation Theory
unitary similarity, Numerical Analysis, Algebra and Number Theory, Canonical forms, reductions, classification, Unitary similarity, 15A21, Frobenius norm, Classification, general position of matrices, 15A21, 15A60, General position, classification of matrices, 15A60, FOS: Mathematics, Discrete Mathematics and Combinatorics, triangular matrices, Geometry and Topology, Representation Theory (math.RT), Mathematics - Representation Theory
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!