TY  - GEN
AU  - Stanimirovic,Ivan
TI  - Computation of generalized matrix inverses
SN  - 9781771886222
U1  - 512.9434 23rd
PY  - 2018///
CY  - Canada
PB  - Apple Academic Press
KW  - Mathematics
KW  - Matrix Algebra
KW  - Matrix Inverses
KW  - Computation
N1  - Includes bibliography and index; Introduction -- Computing generalised inverses of matrices -- Generalised inverses of polynomial and rational matrices -- Applications -- Conclusion
N2  - 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, and covers several methods, such as methods based on full-rank factorization, Leverrier-Faddeev method, method of Zhukovski, and variations of partitioning method

ER  -