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Computation of Generalized Matrix Inverses and Applications
Af: Ivan Stanimirovic Engelsk Paperback
SPAR
kr 159
Computation of Generalized Matrix Inverses and Applications
Af: Ivan Stanimirovic Engelsk Paperback

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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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.

Produktdetaljer
Sprog: Engelsk
Sider: 280
ISBN-13: 9781774630617
Indbinding: Paperback
Udgave:
ISBN-10: 1774630613
Kategori: Algebra
Udg. Dato: 31 mar 2021
Længde: 0mm
Bredde: 229mm
Højde: 152mm
Oplagsdato: 31 mar 2021
Forfatter(e): Ivan Stanimirovic
Forfatter(e) Ivan Stanimirovic


Kategori Algebra


Sprog Engelsk


Indbinding Paperback


Sider 280


Udgave


Længde 0mm


Bredde 229mm


Højde 152mm

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