Say, we had m x n matrix B. B+ is the Moore Penrose Inverse (pseudoinverse) of the matrix. Would B+B (product of pseudoinverse of B and B) be a projection matrix? How would we prove this?
2026-03-26 11:04:57.1774523097
Product of Moore Penrose Inverse and Matrix
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By the defining properties of Moore-Penrose pseudoinverse, $B^+B$ is Hermitian and $$ (B^+B)^2=(B^+BB^+)B=B^+B. $$ Therefore, $B^+B$ is not just a projection, but an orthogonal projection.