Projectors on Intersections of Subspaces

Research output: Chapter in Book/Report/Conference proceedingChapter

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Abstract

Let PL denote the orthogonal projector on a subspace L. Two constructions of projectors on intersections of subspaces are given in finite- dimensional spaces. One construction uses the singular value decomposition of PLPM to give an explicit formula for PL⋂M. The other construction uses the result that the intersection of m ≥ 2 subspaces, L1 ⋂ L2 ⋂ … ⋂Lm, is the null-space of the matrix Q := Σmi=1 λi (I − PLi), for any positive coefficients {λi}. The projector PL1 ⋂ L2 ⋂ … ⋂Lm can then be given in terms of the Moore- Penrose inverse of Q, or as the limit, as t → ∞, of the exponential function exp{−Qt}.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages41-50
Number of pages10
DOIs
StatePublished - 2015

Publication series

NameContemporary Mathematics
Volume636
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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