Characterization of the Oblique Projector $U(VU)^+V$ with Application to Constrained Least Squares

Aleš Černý

doi:10.1016/j.laa.2009.05.025

Characterization of the Oblique Projector $U(VU)^+V$ with Application to Constrained Least Squares

Optimization and Control 2017-07-25 v5 Rings and Algebras

Authors: Aleš Černý

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Abstract

We provide a full characterization of the oblique projector $U(VU)^+V$ in the general case where the range of $U$ and the null space of $V$ are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization.

Keywords

oblique projector constrained least squares pseudoinverse subspace complementarity matrix characterization

Cite

@article{arxiv.0809.4500,
  title  = {Characterization of the Oblique Projector $U(VU)^+V$ with Application to Constrained Least Squares},
  author = {Aleš Černý},
  journal= {arXiv preprint arXiv:0809.4500},
  year   = {2017}
}

Comments

v1: 6 pages v2: 7 pages. Minor changes (formatting, references) in sections 1-2. Extra statement in Theorem 3.1. Substantial revision of section 4 v3: 7 pages. A minor change (more explicit formula for \Xi) in Corollary 4.2. Changed + to direct sum at the bottom of p.5 v4: 7 pages. Removed typo in eq. (17) which was present in v2 and v3

Characterization of the Oblique Projector $U(VU)^+V$ with Application to Constrained Least Squares

Abstract

Keywords

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