Talk:Constrained generalized inverse

Assessment comment

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If

A\in \mathbb {R} ^{m\times n}

then

x\in \mathbb {R} ^{n}

, not

\mathbb {R} ^{m}

--Prime factor (talk) 06:58, 15 October 2008 (UTC)[reply]

== Bott-Duffin inverse ==

Bott-Duffin inverse is defined in a different context. We are looking for a solution of

$Ax+b=c$ ,

$x\in L$ ,

$b\in L^{\perp }$ ,

where $A\in S^{n\times n}$ is a symmetric matrix of order $n\times n$ , $L$ is a linear subspace of order $n$ , $L^{\perp }$ is an orthogonal compliment to $L$ . Then the solution is given by

$x=P_{L}(AP_{L}+P_{L^{\perp }})^{-1}c$ ,

where $P_{L}$ and $P_{L^{\perp }}$ are orthogonal projectors on $L$ and $L^{\perp }$ .

--Prime factor (talk) 07:16, 15 October 2008 (UTC)[reply]

Last edited at 07:16, 15 October 2008 (UTC). Substituted at 01:55, 5 May 2016 (UTC)

Dimensions

The article does not make sense in its current state: matrix A cannot be m-by-n if both x and b are from ℝ^m. — Preceding unsigned comment added by 209.141.188.140 (talk) 12:52, 20 July 2019 (UTC)[reply]