91 citations · 314 across the 15 of their papers we have counts for
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Canonical Forms for Unitary Congruence and *Congruence
Roger A. Horn, Vladimir V. Sergeichuk
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…
Classification of squared normal operators on unitary and Euclidean spaces
Vyacheslav Futorny, Roger A. Horn, Vladimir V. Sergeichuk
We give a canonical form for a complex matrix, whose square is normal, under transformations of unitary similarity as well as a canonical form for a real matrix, whose square is no…
A regularization algorithm for matrices of bilinear and sesquilinear forms
Roger A. Horn, Vladimir V. Sergeichuk
We give an algorithm that uses only unitary transformations and for each square complex matrix constructs a *congruent matrix that is a direct sum of a nonsingular matrix and singu…
Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms
Vyacheslav Futorny, Roger A. Horn, Vladimir V. Sergeichuk
Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices unde…
Canonical matrices of bilinear and sesquilinear forms
Roger A. Horn, Vladimir V. Sergeichuk
Canonical matrices are given for (a) bilinear forms over an algebraically closed or real closed field; (b) sesquilinear forms over an algebraically closed field and over real quate…
Congruences of a square matrix and its transpose
Roger A. Horn, Vladimir V. Sergeichuk
It is known that any square matrix over any field F is congruent to its transpose. We show that they are also *congruent with respect to any nonidentity involution on F.