Evaluating AT,S(2)A_{T,S}^{\left( 2 \right)} Matrix Inverses from full-rank Singular Value Decomposition

Abstract

Based on the compact SVD decomposition of the full rank of a predetermined matrix M, a method for calculating the inverses AT,S(2)A_{T,S}^{\left( 2 \right)} of matrix A is derived. As a consequence, the advantages of compact single value decompositions were developed with this new method. The method is then extended to a set of polynomial matrices. As a result, an algorithm is proposed for effective symbolic computation of AT,S(2)A_{T,S}^{\left( 2 \right)} inverses of a polynomial matrix. Some implementation details and comparative computation times compared to other similar methods are shown to illustrate the efficiency of the algorithm.

Keywords

• generalized inverses
• singular value decomposition
• mathematica
• polynomial matrix
• hermitian matrix
• primary 15a23, 15a09
• secondary 68m40