Abstract
The basic aim of this work is to design a new tridiagonal matrix enhanced multivariance products representation (TMEMPR) which uses not Cartesian vectors but matrices as the support entities. What we obtain after the construction of the representation has been a singular value decomposition like structure where the core matrix becomes a block tridiagonal matrix in contrast to the diagonal and tridiagonal matrix structures of the singular value decomposition of matrices and TMEMPR respectively. We have used support matrices in the construction and not directly orthogonality of the constructed support matrices but block orthogonality which means the mutual ortho normality of the columns of produced support matrices. Certain confirmative implementations finalize the paper.
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