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James E. Tener

  1. Unitary equivalence to a complex symmetric matrix: an algorithm.

    Tue, 08/18/2009 - 11:53 — SomNambul
    Authors: James E. Tener
    Subjects: Functional Analysis
    Abstract

    We present a necessary and sufficient condition for a 3 by 3 matrix to be
    unitarily equivalent to a symmetric matrix with complex entries, and an
    algorithm whereby an arbitrary 3 by 3 matrix can be tested. This test
    generalizes to a necessary and sufficient condition that applies to almost
    every n by n matrix. The test is constructive in that it explicitly exhibits
    the unitary equivalence to a complex symmetric matrix.

  2. On a problem of Halmos: unitary equivalence of a matrix to its transpose.

    Mon, 08/17/2009 - 18:30 — SomNambul
    Authors: Stephan Ramon Garcia, James E. Tener
    Subjects: Functional Analysis
    Abstract

    Motivated by a problem of Halmos, we obtain a canonical decomposition for
    complex matrices which are unitarily equivalent to their transpose (UET).
    Surprisingly, the naive assertion that a matrix is UET if and only if it is
    unitarily equivalent to a complex symmetric matrix (i.e., $T = T^t$) holds for
    matrices 7x7 and smaller, but fails for matrices 8x8 and larger.

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