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    Linear Algebra, 2/e, 2nd Edition

    • Linear Algebra, 2/e, 2nd Edition

    • By: Promode Kumar Saikia

    • Publisher: Pearson Education India

    • Pub. Date:

    • Web ISBN-13: 978-93-325-4084-2

    • Pages in Print Edition: 456

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    Overview

    Designed as a book on Linear Algebra for undergraduate and postgraduate students of mathematics,

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    Top Level Categories:
    Math & Science

    Sub-Categories:
    Math & Science > Algebra

    Table of Contents

     

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    Title Page

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    Contents

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    Preface

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    Preface to the Second Edition

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    A Note to Students

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    List of Symbols

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    Chapter 1: Matrices
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    1.1 Introduction

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    1.2 Basic Concepts

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    1.3 Matrix Operations and Their Properties

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    1.4 Invertible Matrices

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    1.5 Transpose of a Matrix

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    1.6 Partition of Matrices; Block Multiplication

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    1.7 Groups and Fields

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    Chapter 2: Systems of Linear Equations
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    2.1 Introduction

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    2.2 Gaussian Elimination

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    2.3 Elementary Row Operations

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    2.4 Row Reduction

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    2.5 InvertibleMatrices Again

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    2.6 LU Factorization

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    2.7 Determinant

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    Chapter 3: Vector Spaces
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    3.1 Introduction

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    3.2 Basic Concepts

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    3.3 Linear Independence

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    3.4 Basis and Dimension

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    3.5 Subspaces Again

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    3.6 Rank of a Matrix

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    3.7 Orthogonality in ℝn

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    3.8 Bases of Subspaces

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    3.9 Quotient Space

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    Chapter 4: Linear Maps and Matrices
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    4.1 Introduction

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    4.2 Basic Concepts

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    4.3 Algebra of Linear Maps

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    4.4 Isomorphism

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    4.5 Matrices of Linear Maps

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    Chapter 5: Linear Operators
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    5.1 Introduction

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    5.2 Polynomials Over Fields

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    5.3 Characteristic Polynomials and Eigenvalues

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    5.4 Minimal Polynomial

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    5.5 Invariant Subspaces

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    5.6 Some Basic Results

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    5.7 Real Quadratic Forms

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    Chapter 6: Canonical Forms
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    6.1 Introduction

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    6.2 Primary Decomposition Theorem

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    6.3 Jordan Forms

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    Chapter 7: Bilinear Forms
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    7.1 Introduction

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    7.2 Basic Concepts

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    7.3 Linear Functionals and Dual Space

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    7.4 Symmetric Bilinear Forms

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    7.5 Groups Preserving Bilinear Forms

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    Chapter 8: Inner Product Spaces
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    8.1 Introduction

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    8.2 Hermitian Forms

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    8.3 Inner Product Space

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    8.4 Gram–Schmidt Orthogonalization Process

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    8.5 Adjoints

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    8.6 Unitary and Orthogonal Operators

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    8.7 Normal Operators

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    Bibliography

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    Copyright