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

Aleš Černý

doi:10.1016/j.laa.2009.05.025

paper

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

arXiv:0809.4500 · doi:10.1016/j.laa.2009.05.025

Abstract

We provide a full characterization of the oblique projector $U (V U)^{+} V$ 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.

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 Ξ) 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

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