Advances in linear algebra research / Ivan Kyrchei, editor.

Format:

Book

Contributor:

Kyrchei, Ivan, editor.

Series:

Mathematics research developments series.

Mathematics Research Developments

Language:

English

Subjects (All):

Algebras, Linear.

Physical Description:

1 online resource (367 p.)

Place of Publication:

New York, New York : Nova Science Publishers, Inc., 2015.

Language Note:

English

Summary:

This book presents original studies on the leading edge of linear algebra. Each chapter has been carefully selected in an attempt to present substantial research results across a broad spectrum. The main goal of Chapter One is to define and investigate the restricted generalized inverses corresponding to minimization of constrained quadratic form. As stated in Chapter Two, in systems and control theory, Linear Time Invariant (LTI) descriptor (Differential-Algebraic) systems are intimately related to the matrix pencil theory. A review of the most interesting properties of the Projective Equival

Contents:

""ADVANCES IN LINEAR ALGEBRA RESEARCH""; ""ADVANCES IN LINEAR ALGEBRA RESEARCH""; ""LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA""; ""CONTENTS""; ""PREFACE""; ""Chapter 1: MINIMIZATION OF QUADRATIC FORMS AND GENERALIZED INVERSES""; ""Abstract""; ""1. Introduction""; ""2. Overview of Known Results of Quadratic Optimization and Preliminary Results""; ""3. The T-RestrictedWeightedMoore-Penrose Inverse""; ""4. The T-RestrictedWeighted Drazin Inverse""; ""5. Some Possible Perspectives""; ""6. Conclusion""; ""References""

""Chapter 2: THE STUDY OF THE INVARIANTSOF HOMOGENEOUS MATRIX POLYNOMIALS USINGTHE EXTENDED HERMITE EQUIVALENCE""""Abstract""; ""1. Introduction""; ""2. Significant Properties of the Set of SE Invariants under BE""; ""3. Projective Equivalence of Homogeneous Binary Polynomials""; ""4""; ""References""; ""Chapter 3: CRAMER�S RULEFOR GENERALIZED INVERSE SOLUTIONS""; ""Abstract""; ""1. Preface""; ""2. Analogues of the Classical Adjoint Matrix for Generalized Inverse Matrices""; ""3. Cramer�s Rules for Generalized Inverse Solutions of Systems of Linear Equations""

""4. Cramer�s Rule of the Generalized Inverse Solutions of Some Matrix Equations""""5. An Application of the Determinantal Representations of the Drazin Inverse to Some DifferentialMatrix Equations""; ""6. Conclusion""; ""References""; ""Chapter 4: FEEDBACK ACTIONS ON LINEAR SYSTEMS OVER VON NEUMANN REGULAR RINGS""; ""Abstract""; ""1. Introduction""; ""2. Preliminaries: What is Known for Fields?""; ""3. Derivation of a Canonical Form""; ""4. Simultaneous Solution to Reach and Pols""; ""5. Other Techniques and FutureWork""; ""6. Conclusion""; ""References""

""Chapter 5: HOW TO CHARACTERIZE PROPERTIESOF GENERAL HERMITIAN QUADRATICMATRIX-VALUED FUNCTIONS BY RANKAND INERTIA""""Abstract""; ""1. Introduction""; ""2. Preliminaries""; ""3. Basic Formulas""; ""4. The Convexity and Concavity of Hermitian Matrix-Valued Fuction""; ""5. Two Types of Multiple HQMVF""; ""Some Optimization Problems on the Matrix EquationAXB""; ""7. Concluding Remarks""; ""Acknowledgments""; ""References""; ""Chapter 6: INTRODUCTION TO THE THEORYOF TRIANGULAR MATRICES (TABLES)""; ""Abstract""; ""1. Preface""; ""2. Combinatorial Preliminaries""

""3. Definition of TriangularMatrices and Functions on Them""""3.32)4. Properties of Parafunctions of""; ""5. On Relation of Parafunctions with Other Functions of Matrices""; "".6. Some Theorems on Applying TriangularMatrix""; ""7. Conclusion""; ""References""; ""Chapter 7: RECENT DEVELOPMENTSIN ITERATIVE ALGORITHMS FOR SOLVING LINEARMATRIX EQUATIONS""; ""Abstract""; ""1. Introduction""; ""2. The Matrix Form of CGNE Algorithm""; ""3. The Gradient Iterative Algorithms""; ""4. The Matrix Form of LSQR Algor""; ""4. The Matrix Form of LSQR Algorithms""

""5. The Matrix Form of Bi-CG and Bi-CR Algorithms""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-63463-580-9

OCLC:

902846987