Maximal orthogonality and pseudo-orthogonality with applications to generalized inverses
type: Item
instance of: scholarly article
title: Maximal orthogonality and pseudo-orthogonality with applications to generalized inverses
zbMATH Open document ID: 0961.15020
DOI: 10.1016/S0024-3795(00)00142-7
published in: Linear Algebra and its Applications
publication date: 2001-01-11T00:00:00Z
review text: A finite-dimensional vector space \(V\) over a field \(F\) with a nondegenerate symmetric bilinear, alternating bilinear or Hermitian form, with the subspace \(U\) of \(V\) is considered. The subspace \(U\) admits a pseudo-orthogonal complementary subspace \(U^C\). Constructing a pseudo-orthogonal complement is discussed. A maximally orthogonal subspace is introduced. The characterization of pseudo-orthogonal complements on \(V\) is described. Counting maximally orthogonal complements and pseudo-orthogonal complements is carried out. Vectors occurring in some maximally othogonal or pseudo-orthogonal complements are characterized. Moore-Penrose inverses and generalized inverses are computed.
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 1523268
zbMATH Keywords: matrix inversion
zbMATH Keywords: bilinear forms
zbMATH Keywords: pseudo-orthogonal complement
zbMATH Keywords: maximally orthogonal complement
zbMATH Keywords: Hermitian form
zbMATH Keywords: Moore-Penrose inverses
zbMATH Keywords: generalized inverses
author: Michael Q. Rieck
MaRDI profile type: Publication
cites work: Q3241211
cites work: Q3992965
cites work: Q5576154
cites work: Totally isotropic subspaces, complementary subspaces, and generalized inverses
cites work: Existence of generalized inverse of linear transformations over finite fields
description: scientific article; zbMATH DE number 1523268