Computation of Generalized Matrix Inverses and Applications

Ivan Stanimirović

December 13, 2017 by Apple Academic Press
Reference - 280 Pages - 2 B/W Illustrations
ISBN 9781771886222 - CAT# N11963

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  • Provides in-depth coverage of important topics in matrix theory and generalized inverses of matrices, highlighting the Moore-Penrose inverse
  • Requires no prior knowledge of linear algebra
  • Offers an extensive collection of numerical examples on numerical computations
  • Describes several computational techniques for evaluating matrix full-rank decompositions, which are then used to compute generalized inverses
  • Highlights popular algorithms for computing generalized inverses of both polynomial and constant matrices
  • Presents several comparisons of performances of methods for computing generalized inverses
  • Includes material relevant in theory of image processing, such as restoration of blurred images
  • Shows how multiple matrix decomposition techniques can be exploited to derive the same result


This volume offers a gradual exposition to matrix theory as a subject of linear algebra. It presents both the theoretical results in generalized matrix inverses and the applications. The book is as self-contained as possible, assuming no prior knowledge of matrix theory and linear algebra.

The book first addresses the basic definitions and concepts of an arbitrary generalized matrix inverse with special reference to the calculation of {i,j,...,k} inverse and the Moore–Penrose inverse. Then, the results of LDL* decomposition of the full rank polynomial matrix are introduced, along with numerical examples. Methods for calculating the Moore–Penrose’s inverse of rational matrix are presented, which are based on LDL* and QDR decompositions of the matrix. A method for calculating the A(2)T;S inverse using LDL* decomposition using methods is derived as well as the symbolic calculation of A(2)T;S inverses using QDR factorization.

The text then offers several ways on how the introduced theoretical concepts can be applied in restoring blurred images and linear regression methods, along with the well-known application in linear systems. The book also explains how the computation of generalized inverses of matrices with constant values is performed. It covers several methods, such as methods based on full-rank factorization, Leverrier–Faddeev method, method of Zhukovski, and variations of the partitioning method.