Linear Algebra, 2e.

Format:

Book

Author/Creator:

Saikia, Promode Kumar.

Language:

English

Subjects (All):

Algebras, Linear--Textbooks.

Algebras, Linear.

Physical Description:

1 online resource (457 pages)

Edition:

2nd ed.

Place of Publication:

Noida : Pearson India, 2014.

Summary:

Designed for undergraduate and postgraduate students of Mathematics, Linear Algebra, 2eexplains the basics comprehensively and with clarity. The flowing narrative of the book provides a refreshing approach to the subject. Drawing on decades of teaching experience and extensive discussions with teachers and students, this book simplifies mathematical proofs while doing away with unnecessary details.

Contents:

Cover

Copyright

Contents

Preface

Preface to the Second Edition

A Note to Students

List of Symbols

Matrices

1.1INTRODUCTION

1.2BASIC CONCEPTS

1.3 MATRIX OPERATIONS AND THEIR PROPERTIES

1.4 INVERTIBLE MATRICES

1.5 TRANSPOSE OF A MATRIX

1.6 PARTITION OF MATRICES

BLOCK MULTIPLICATION

1.7 GROUPS AND FIELDS

Systems of LinearEquations

2.1 INTRODUCTION

2.2 GAUSSIAN ELIMINATION

2.3 ELEMENTARY ROW OPERATIONS

2.4 ROW REDUCTION

2.5 INVERTIBLE MATRICES AGAIN

2.6 LU FACTORIZATION

2.7 DETERMINANT

Vector Spaces

3.1 INTRODUCTION

3.2 BASIC CONCEPTS

3.3 LINEAR INDEPENDENCE

3.4 BASIS AND DIMENSION

3.5 SUBSPACES AGAIN

3.6 RANK OF A MATRIX

3.7 ORTHOGONALITY IN Rn

3.8 BASES OF SUBSPACES

3.9 QUOTIENT SPACE

Linear Mapsand Matrices

4.1 INTRODUCTION

4.2 BASIC CONCEPTS

4.3 ALGEBRA OF LINEAR MAPS

4.4 ISOMORPHISM

4.5 MATRICES OF LINEAR MAPS

Linear Operators

5.1 INTRODUCTION

5.2 POLYNOMIALS OVER FIELDS

5.3 CHARACTERISTIC POLYNOMIALS AND EIGENVALUES

5.4 MINIMAL POLYNOMIAL

5.5 INVARIANT SUBSPACES

5.6 SOME BASIC RESULTS

5.7 REAL QUADRATIC FORMS

Canonical Forms

6.1 INTRODUCTION

6.2 PRIMARY DECOMPOSITION THEOREM

6.3 JORDAN FORMS

Bilinear Forms

7.1 INTRODUCTION

7.2 BASIC CONCEPTS

7.3 LINEAR FUNCTIONALS AND DUAL SPACE

7.4 SYMMETRIC BILINEAR FORMS

7.5 GROUPS PRESERVING BILINEAR FORMS

Inner Product Spaces

8.1 INTRODUCTION

8.2 HERMITIAN FORMS

8.3 INNER PRODUCT SPACE

8.4 GRAM-SCHMIDT ORTHOGONALIZATION PROCESS

8.5 ADJOINTS

8.6 UNITARY AND ORTHOGONAL OPERATORS

8.7 NORMAL OPERATORS

Bibliography

Index

Blank Page.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

93-325-4052-7

OCLC:

1024280763