Classification of sesquilinear forms, pairs of Hermitian forms, self- conjugate and isometric operators over the division ring of quaternions

DOI10.1007/BF01158220zbMath0774.15010MaRDI QIDQ687368

V. V. Sergejchuk

Publication date: 21 October 1993

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Hermitian formsnonstandard involutionsesquilinear formsdivision algebra of quaternionsfinite- dimensional vector spacesself- adjoint and isometric operators

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Quadratic and bilinear forms, inner products (15A63)

Related Items (7)

$m$th roots of $H$-selfadjoint matrices over the quaternions ⋮ Canonical forms for mixed symmetric-skewsymmetric quaternion matrix pencils ⋮ Pairs of Hermitian and skew-Hermitian quaternionic matrices: canonical forms and their applications ⋮ Canonical matrices of isometric operators on indefinite inner product spaces ⋮ Canonical matrices of bilinear and sesquilinear forms ⋮ Basic classes of matrices with respect to quaternionic indefinite inner product spaces ⋮ Pairs of quaternionic selfadjoint operators with numerical range in a halfplane

Cites Work

• Classification of pairs consisting of a linear and a semilinear map
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