The article presents a formalism to define non-trivial subspaces of complex matrix spaces of order m by n, where m and n are different. This is achieved by using the Spacer matrix( as defined in Ghosh[1]) and it’s Hermitian conjugate, associated with the matrix space, as the building blocks. The Mathematical formalism is presented and illustrated with suitable numerical examples.

Keywords : Spacer Matrices, Component Matrices of the Spacer Matrix, Embedding Dimension, Spacer Matrix based Generalized Matrix Multiplication.