Talk:Orthogonal projection

Doesn't the formula become the identity matrix?

$M(M^{\top }M)^{-1}M^{\top }=MM^{-1}{(M^{\top })}^{-1}M^{\top }=E$

-- Bernhard Bauer

No, because M is not a square matrix, but rather M has (typically many) more rows than columns. Michael Hardy 19:05, 19 Apr 2004 (UTC)