The article presents a Generalized Matrix Multiplication scheme that allows Non-compatible matrices to be multiplied using Spacer matrices, which are unique for every possible pair of nonconforming dimensions. The article presents an approach to define positive integral powers of strictly rectangular complex matrices and thereby define subspaces of the Complex Matrix space using these matrix powers to constitute the pertinent spanning sets. The mathematical formalism is presented and Illustrated with numerical examples

Keywords : Matrix Multiplication, Generalized Matrix Multiplication, Embedding Dimension, Spacer Matrix, Components of the Spacer Matrix