91 citations · 234 across the 5 of their papers we have counts for
5 papers
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.
Canonical forms for complex matrix congruence and *congruence
Roger A. Horn, Vladimir V. Sergeichuk
Canonical forms for congruence and *congruence of square complex matrices were given by Horn and Sergeichuk in [Linear Algebra Appl. 389 (2004) 347-353], based on Sergeichuk's pape…