Canonical forms for complex matrix congruence and ∗congruence
By Roger A. Horn, V. Sergeichuk. 2006
114 citations recorded by the source corpus.
Abstract 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 paper [Math. USSR, Izvestiya 31 (3) (1988) 481–501], which employed the theory of representations of quivers with involution. We use standard methods of matrix analysis to prove directly that these forms are canonical. Our proof provides explicit algorithms to compute all the blocks and parameters in the canonical forms. We use these forms to derive canonical pairs for simultaneous congruence of pairs of complex symmetric and skew-symmetric matrices as well as canonical forms for simultaneous ∗congruence of pairs of complex Hermitian matrices.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/5bdbc747a6fd25f2ccc552f433c91686c2ec6108
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
- Froilán M. Dopico
- Fernando De Terán
- Roger A. Horn
- V. Sergeichuk
- Valeria Simoncini
- An M. Dopico
- Fernando De Ter
- G. Belitskii
In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Froilán M. Dopico
- Fernando De Terán
- V. Sergeichuk
- Roger A. Horn
- Valeria Simoncini
- An M. Dopico
- Fernando De Ter
Citations in the corpus
- The solution of the equation XA + AXT = 0 and its application to the theory of orbits (2011, methodology): “Section 2 presents some preliminaries and introduces the canonical form for congruence [17].”
- Canonical matrices of bilinear and sesquilinear forms (2007, background): “Such a simplification was given by the authors in [9] for canonical matrices of bilinear and sesquilinear forms over C; a direct proof that the matrices from [9] are canonical is given in [10, 11]; applications of these canonical matrices were obtained in [3, 4, 5, 11, 12].”