Maximal orthogonality and pseudo-orthogonality with applications to generalized inverses
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.
scientific article; zbMATH DE number 1523268