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A First Course in Linear Algebra  
Author(s): Aloknath Chakrabarti
Published by Vijay Nicole Imprints Private Limited
Publication Date:  Available in all formats
ISBN: 9789394681774

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ISBN: 9788182091306 Price: INR 495.00
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Table of contents

Biographical note

Linear Algebra is of extreme importance in mathematics and has applications in almost all branches of science and engineering. This book exposes you to the subject at the fundamental level as learnt by undergraduate and postgraduate students of mathematics.

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Description

Linear Algebra is of extreme importance in mathematics and has applications in almost all branches of science and engineering. This book exposes you to the subject at the fundamental level as learnt by undergraduate and postgraduate students of mathematics.

Table of contents
  • Cover
  • Halftitle Page
  • Title Page
  • Copyright Page
  • Dedication Page
  • Contents
  • Preface
  • 1. Matrices and their Uses
    • Basic Definitions and Concepts
    • Algebraic Operations Involving Matrices
    • The Gaussian Method (and the Gauss-Jordan method)
    • The Inverse of a Square Matrix
    • The Gaussian Method
    • Exercise
  • 2. Determinats and their Uses
    • Basic Definitions
    • Simplifications to Evaluate Determinants
    • Properties of Determinants
    • Inverse of Matrices Using Determinants—Cramer's Rule
    • Exercise
  • 3. The Euclidean Vector Spaces
    • Euclidean n-space (Rn)
    • Linear Transformations from Rn to Rm
    • Important Results Involving Linear Transformations
    • Exercise
  • 4. General Vector Spaces
    • Real Vector Spaces
    • Basis and Dimension
    • The Four Fundamental Spaces
    • Rank and Nullity
    • Exercise
  • 5. Inner-Product Spaces
    • Inner-product in General
    • Orthogonality
    • Orthogonal and Orthonormal Basis—Gram-Schmidt Process
    • Least Squares Solution
    • Orthogonal Matrices
    • Exercise
  • 6. Eigenvalue Problems and their Applications
    • Basic Definitions
    • Diagonalization of Square Matrices
    • Orthogonal Diagonalization
    • Application of Diagonalization
    • Some Special Results
    • Exercise
  • 7. Worked Out Problems
    • Worked Out Problems Involving Chapter 1
    • Worked Out Problems Involving Chapter 2
    • Worked Out Problems Involving Chapter 3
    • Worked Out Problems Involving Chapter 4
    • Worked Out Problems Involving Chapter 5
    • Worked Out Problems Involving Chapter 6
  • Index
Biographical note
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