Calculation of a Constrained Minimal Symmetric Matrix

TLDR: In this paper, a procedure is derived for calculating a symmetric matrix P with minimal sum of the squares of its elements, which satisfies the condition that B and A are rectangular or square matrices.

Abstract: A procedure is derived for calculating a symmetric matrix, P, with minimal sum of the squares of its elements, which satisfies $PB = A$. B and A are rectangular or square matrices. It is necessary that $AB^ + B = A$, which is not a trivial requirement if B has more columns than rows, or if B is not of full rank. Also, no solution is possible unless $B'A$ is symmetric. The procedure is similar to that for calculating a nonsymmetric minimal matrix, but with additional terms to give symmetry.