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斜投影器$U(VU)^+V$的特征及其在约束最小二乘中的应用

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

Aleš Černý

备注：
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
发表信息：
Linear Algebra and Its Applications 2009, 431(9), 1564-1570
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摘要：

我们提供了一个完整的表征斜投影仪$U(VU)^+V$在一般情况下，范围的$U$和零空间的$V$不是互补的子空间。我们讨论的约束最小二乘极小化的背景下，新的结果。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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