A Mathematical Scheme Defined On Strictly Rectangular Complex Matrix Spaces Involving Frobenius Norm Preservation under the Possibility of Matrix Rank Readjustment and Internal Redistribution of Variance using Spacer Component Matrices and a Completely Positive Trace Preserving Transformation

The Research paper presents a mathematical framework on strictly rectangular complex matrix spaces that preserve the Frobenius norm but allow for possible readjustment of variance contribution per degrees of freedom as a result of allowed flexibility of the rank modification and alteration of the Principal axes. This is achieved through the utilization of Spacer component matrices and matrices generated from them and the use of a specific Completely Positive Trace preserving transformation determined solely based on the embedding dimension, which is the order of the embedded square matrix space associated with the strictly rectangular input matrix space.