Characterization of the Oblique Projector $U(VU)^+V$ with Application to Constrained Least Squares
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2008
- DOI:
- 10.48550/arXiv.0809.4500
- arXiv:
- arXiv:0809.4500
- Bibcode:
- 2008arXiv0809.4500C
- Keywords:
-
- Mathematics - Optimization and Control;
- Mathematics - Rings and Algebras;
- 15A09;
- 15A04;
- 90C20
- E-Print:
- 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