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Computation of Generalized Matrix Inverses and Applications (Paperback)
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Computation of Generalized Matrix Inverses and Applications (Paperback)
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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.
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