Canonical matrices of bilinear and sesquilinear forms
By Roger A. Horn, V. Sergeichuk. 2007
52 citations recorded by the source corpus.
Abstract Canonical matrices are given for (i) bilinear forms over an algebraically closed or real closed field; (ii) sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and (iii) sesquilinear forms over a field F of characteristic different from 2 with involution (possibly, the identity) up to classification of Hermitian forms over finite extensions of F ; the canonical matrices are based on any given set of canonical matrices for similarity over F . A method for reducing the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings is used to construct the canonical matrices. This method has its origins in representation theory and was devised in [V.V. Sergeichuk, Classification problems for systems of forms and linear mappings, Math. USSR-Izv. 31 (1988) 481–501].
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/140373216f2312540abab41c52b3d009e7764e4d
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In Algebra and Number Theory
In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- The solution of the equation XA + AXT = 0 and its application to the theory of orbits (2011, methodology): “In this work we compute the dimension of the solution space of (1) and describe how to find this solution space through the following procedure: (a) we show how the solution space of (1) is transformed under congruence of A and prove that its dimension remains invariant; (b) we transform A into its ”