Singular Value Decomposition for Multidimensional Matrices

Singular Value Decomposition (SVD) is of great significance in theory development of mathematics and statistics. In this paper we propose the SVD for 3-dimensional (3-D) matrices and extend it to the general Multidimensional Matrices (MM). We use the basic operations associated with MM introduced by Solo to define some additional aspects of MM. We achieve SVD for 3-D matrix through these MM operations. The proposed SVD has similar characterizations as for 2-D matrices. Further we summarize various characterizations of singular values obtained through the SVD of MM. We demonstrate our results with an example and compare them with the existing method. We also develop Matlab functions to perform SVD of MM and some related MM operations.