Theory of matrices / B. S. Vatsa, Suchi Vatsa.

Format:

Book

Author/Creator:

Vatsa, B. S., author.

Vatsa, Suchi, author.

Language:

English

Subjects (All):

Matrices.

Physical Description:

1 online resource (334 p.)

Edition:

Fourth edition.

Place of Publication:

Kent, [England] : New Academic Science Limited, 2013.

Language Note:

English

Summary:

Basic definitions, principles and theorems followed by numerical illustrations. Discusses algebra and matrices from the beginning. Chapters on Bilinear forms, Quadratic forms, Hermitian forms included for computer, engineering and economics and advanced studies.

Contents:

Cover

Preface

Contents

Chapter 1 Matrices

1.1 Definition and Examples of a Matrix

1.2 Diagonal, Scalar,Unit, And Triangular Matrix

1.3 Equal and Unequal Matrices

1.4 The Transpose of a Matrix: Symmetric and Skew-Symmetric

1.5 The Conjugate of a Matrix: Hermitian and Skew-Hermitian Matrices

1.6 Submatrics

Submatrices

Chapter 2 Algebra of Matrices

2.1 Addition of Two Matrices

2.2 Properties of Addition

2.3 Scalar Multiples of Matrices

2.4 Multiplication of Matrices

2.5 The Properties of Matrix Multiplication

2.6 Powers of Matrices: Laws of Exponents

2.7. Idempotent, Nilpotent, Involutory, Orthogonal And Unitary Matrices

Chapter 3 Determinants

3.1 Definition

3.2 Minors and Cofactors

3.3 Properties of Determinants

3.4 Laplace's Expansions

3.5 Symmetric and Skew-Symmetric Determinant

3.6 Product of Two Determinants

3.7 Reciprocal Determinant

Chapter 4 Adjoint and Inverse of a Matrix

4.1 Definition and Examples

4.2 Inverse of a Matrix

4.3 Linear Computations

4.4 Partitioning of Matrices

Chapter 5 Rank and Equivalence

5.1 The Concept of a Rank

5.2 Elementary Transformations

5.3 Equivalent Matrices

5.4 Elementary Matrices

5.5 Normal Form

5.6 Elementary Transformation by Matrix Multiplication

5.7 Computation of The Inverse of Matrix by Elementary Transformation

Chapter 6 Linear Equations

6.1 System of Linear Equations and Consistency

6.2 Solution of n Linear Equations In n Unknowns

6.3 Solution of m Linear Equations In n Unknowns With m &lt

n and m &gt

n

6.4 Homogeneous Linear Equations

Chapter 7 Vector Spaces and Linear Transformations

7.1 Definition of a Vector and Vector Spaces

7.2 Vector Space Spanned by a Given System of Vectors

7.3 Linearly Dependent and Linearly Independent System of Vectors.

7.4 Basis and Dimension

7.5 Subspace

7.6 Row and Column Space of a Matrix

7.7 Linear Transformations

7.8 Operators on Vnn

7.9 Geometric Transformation

7.10 Geometric Properties of Plane Linear Transformation

7.11 Rotation

7.12 Reflection

7.13 Expansions and Compressions

7.14 Shears

7.15 Translation

7.16 Successive Transformations

7.17 Inverse Transformation

Chapter 8 Characteristic Roots and Vectors of a Matrix

8.1 Definition and Examples

8.2 Properties of The Characteristic Polynomial

8.3 Application of the Cayley-Hamilton Theorem In Finding Out The Inverse of a Non-Singular Matrix

8.4 The Minimum Polynomial of a Matrix

8.5 Characteristic Roots and Vectors of a Square Matrix

8.6 Characteristic Roots of Polynomial Function of a Matrix A

8.7 Characteristic Roots of Special Matrices

8.8 The Diagonal Form of a Hermitian Matrix

Chapter 9 Bilinear Forms

9.1 Bilinear Forms

9.2 The Equivalence of Bilinear Forms

9.3 Types of Bilinear Forms

9.4 Cogredient Transformations

9.5 Contragredient Transformations

Chapter 10 Quadratic Forms

10.1 Quadratic Forms

10.2 Linear Transformation

10.3 Reduction of Real Quadratic Form to Normal (or Canonical) Form

10.4 Lagrange's Reduction

10.5 Regular Quadratic Forms

10.6 Kronecker's Method of Reduction

10.7 Sylvester's Law of Inertia of Quadratic Forms

10.8 Definite, Semi-Definite and Indefinite Real Quadratic Forms

10.9 Definite Matrices

10.10 A Necessary and Sufficient Condition for Positive Definiteness

Chapter 11 Hermitian Forms

11.1 Hermitian Forms

11.2 Definite Hermitian Form

Chapter 12 Similar Matrices

12.1 Similar Matrices

12.2 Diagonal Matrices

Answers to Problems

Index.

Notes:

Includes index.

Description based on online resource; title from PDF title page (ebrary, viewed September 8, 2015).

ISBN:

1-78183-052-5

OCLC:

919481093