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Introduction to Matrix Theory

Introduction to Matrix Theory

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INTRODUCTION TO MATRIX THEORY discusses a range of applications in Statistics, Combinatorial Science, Functional and Numerical Analysis etc. The fundamental properties of Matrix Theory blended with the Linear Algebraic Theory have been applied with a view to analysing practical algorithms in many algebraic problems. The problems discussed in the book find their relevance in solving daily life problems. The techniques applied herein considerably overlap with analytic algebraic theory as reflected in the topics related to functional analysis. This book is not simply aimed at confining itself to computational matrix but addresses some of the algebraic techniques relevant to functional theory and offers an introduction to important aspects of Matrix Theory.

Preface / Acknowledgement / Introductory Chapter / Transposition ad Conjugation of Matrices / Determinants / Inverse of a Matrix / Simultaneous Linear Equations / System of Non-homogeneous Linear Equations / Similarity of Matrices (Part-I) / Similarity of Matrices (Part-II) / Similarity of Matrices (Part-III) / Bilinear Forms / Vector Spaces (Part-I) / Vector Spaces (Part-II) / Vector Subspace / Linear combination of Vectors / Quotient Space and Direct Sum of Subspaces / Basis and Dimension of a Vector Space / Linear Dependence and linear Independence / Linear Transformation: Vector Space of L.T. / Adjoint of a Linear Transformation / Matrix of a Linear Transformation / Eigenvectors and Eigenvalues of Linear Transformation.

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