On Singular Value Decomposition of Rectangular Matrices

The singular value decomposition of matrices stands as one of the most important concepts in mathematics, because of its variety of applications in mathematics, statistics, biology and many other areas of science. In this thesis, we present the singular value decomposition and its relation to the spectral decomposition . We also investigate the singular value decomposition of a matrix together with some of its applications. Some of these applications include the Moore-Penrose psuedoinverse, the effective rank of matrices and image compression.