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We use methods of the general theory of congruence and *congruence for complex matrices--regularization and cosquares-to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices A such that \bar{A}A (respectively, A^2) is normal.
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H. Faßbender and Kh. D. Ikramov, Some observations on the Youla form and conjugate-normal matrices, Linear Algebra Appl. (2006) IN PRESS
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R. A. Horn and V. V. Sergeichuk, A regularization algorithm for matrices of bilinear and sesquilinear forms, Linear Algebra Appl. 412 (2006) 380-395
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R. A. Horn and V. V. Sergeichuk, Canonical forms for complex matrix congruence and *congruence, Linear Algebra Appl. 416 (2006) 1010-1032
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