Matrices | by V. N. Kala and Rajeshri Rana | 2009 | ISBN: 9788131807026. Mathematics Books. Mathematical Physics Books. SOLUTION OF THE SYSTEM OF HOMOGENEOUS LINEAR EQUATIONS. COMPUTATION OF INVERSE OF A MATRIX BY ELEMENTARY TRANSFORMATION. THEOREMS ON RANK OF A MATRIX. Cayley Hamilton Theorem

March 13, 2010 by kutenk
Filed under: Business Books, Engineering Books 

Matrices

by V. N. Kala and Rajeshri Rana
2009 (177 pages)
ISBN:9788131807026

Written in an innovative style, this lucid and comprehensive book is a complete treatise on Real Mathematics portion-matrices, which also serves a vital role in Mathematical Physics and various other scientific fields.

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Matrices







Preface
Foreword
Chapter 1 – Introduction to Matrices
1.1: MATRIX: DEFINITION
1.2: MATRICES: IT’S TYPES
1.3: EQUALITY OF MATRICES
1.4: ADDITION OF MATRICES
1.5: PROPERTIES OF MATRIX ADDITION
1.6: SCALAR MULTIPLICATION OF A MATRIX
1.7: MATRIX MULTIPLICATION
1.8: PROPERTIES OF MATRIX MULTIPLICATION
1.9: POSITIVE INTEGRAL POWER OF A SQUARE MATRIX
1.10: ZERO DIVISORS




Chapter 2 – Some Special Types of Matrices
2.1: TRANSPOSE OF MATRIX
2.2: SYMMETRIC MATRIX
2.3: SKEW-SYMMETRIC MATRIX
2.4: COMPLEX MATRIX
2.5: THEOREMS
2.6: CONJUGATE OR TRANJUGATE OF MATRIX
2.7: HERMITIAN AND SKEW HERMITIAN MATRIX
2.8: THEOREMS
2.9: IDEMPOTENT MATRIX
2.10: NILPOTENT MATRIX
2.11: INVOLUTARY MATRIX
2.12: ORTHOGONAL MATRIX
2.13: UNITARY MATRIX
2.14: SINGULAR MATRIX
2.15: THEOREMS
2.16: ORTHOGONAL MATRICES
2.17: THEOREMS
2.18: ADJOINT AND INVERSE OF A MATRIX
2.19: THEOREMS
2.20: INVERSE OF MATRIX
2.21: THEOREMS

Chapter 3 – Elementary Transformations
3.1: ELEMENTARY TRANSFORMATION
3.2: ELEMENTARY MATRICES
3.3: ELEMENTARY OPERATIONS AS MATRIX PRODUCTS
3.4: THEOREMS ON ELEMENTARY OPERATIONS
3.5: EQUIVALENT MATRICES
3.6: THEOREMS
3.7: COMPUTATION OF INVERSE OF A MATRIX BY ELEMENTARY TRANSFORMATION
3.8: TRIANGULAR MATRIX
3.9: REDUCTION OF MATRICES TO TRIANGULAR FORM
3.10: PARTITIONING OF MATRICES
3.11: IDENTICALLY PARTITIONED MATRICES
3.12: MATRICES PARTITIONED CONFORMABLY FOR MULTIPLICATION

Chapter 4 – Rank of a Matrix
4.1: MINOR OF A MATRIX
4.2: RANK OF A MATRIX
4.3: NULLITY OF A MATRIX
4.4: EQUIVALENT MATRICES POSSESS SAME RANK
4.5: NORMAL FORM OF A MATRIX
4.6: THEOREMS ON RANK OF A MATRIX
4.7: ZERO ROW AND NON-ZERO ROWS
4.8: ECHELON FORM OF A MATRIX
4.9: RANK OF MATRIX IN ECHELON FORM

Chapter 5 – Simultaneous Linear Equations
5.1: SIMULTANEOUS LINEAR EQUATIONS
5.2: WORKING RULE TO FIND THE SOLUTION OF THE SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS
5.3: SOLUTION OF SYSTEM OF NON-HOMOGENEOUS LINEAR EQUATIONS IN N-UNKNOWNS
5.4: THEOREM ON CONSISTENCY OF EQUATIONS
5.5: SOLUTION OF THE SYSTEM OF HOMOGENEOUS LINEAR EQUATIONS

Chapter 6 – Linear Dependence of Vectors
6.1: ORDERED SET OF NUMBERS
6.2: VECTORS: n DIMENSIONAL VECTOR
6.3: EQUAL VECTORS
6.4: ROW VECTOR AND COLUMN VECTOR
6.5: NULL VECTOR
6.6: VECTOR ADDITION AND SCALAR MULTIPLICATION
6.7: NEGATIVE OF VECTOR
6.8: VECTOR SPACE OVER A FIELD
6.9: LINEAR DEPENDENCE AND INDEPENDENCE OF VECTORS
6.10: LINEAR COMBINATION OF VECTORS
6.11: BASIS AND DIMENSIONS OF A VECTOR SPACE
6.12: THEOREMS ABOUT LINEAR DEPENDENCE OF VECTORS
6.13: LINEAR TRANSFORMATION




Chapter 7 – Characteristic Roots and Characteristic Vectors
7.1: MATRIX POLYNOMIAL HAVING DEGREE n
7.2: CHARACTERISTIC VALUE PROBLEM
7.3: CHARACTERISTIC MATRIX
7.4: CHARACTERISTIC POLYNOMIAL
7.5: CHARACTERISTIC EQUATION
7.6: CHARACTERISTIC ROOTS AND CHARACTERISTIC VECTORS
7.7: PROPERTIES OF EIGEN VALUES/CHARACTERISTIC ROOTS
7.8: WORKING RULE TO FIND CHARACTERISTIC ROOTS AND CHARACTERISTIC VECTORS OF A MATRIX
7.9: FUNDAMENTAL THEOREMS




Chapter 8 – Cayley Hamilton Theorem
8.1: CHARACTERISTIC EQUATION OF A MATRIX
8.2: CAYLEY HAMILTON THEOREM
8.3: INVERSE COMPUTATION BY CAYLEY HAMILTON THEOREM

Chapter 9 – Diagonalisation of Matrices
9.1: MATRICES SIMILARITY
9.2: THEOREMS ON MATRICES SIMILARITY
9.3: DIAGONALIZABLE MATRIX
9.4: WORKING RULE FOR DIAGONALIZATION OF MATRIX OF ORDER n × n
9.5: THEOREMS ON DIAGONALIZABLE MATRICES

Chapter 10 – Matrices & Determinants
10.1: MATRICES
10.2: DETERMINANT OF A MATRIX
10.3: DIFFERENCE BETWEEN MATRICES AND DETERMINANT
10.4: DETERMINANT: IT’S GENERAL DEFINITION:
10.5: GENERAL PROPERTIES OF THE DETERMINANTS
10.6: APPLICATION OF DETERMINANTS

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Comments

One Comment on Matrices | by V. N. Kala and Rajeshri Rana | 2009 | ISBN: 9788131807026. Mathematics Books. Mathematical Physics Books. SOLUTION OF THE SYSTEM OF HOMOGENEOUS LINEAR EQUATIONS. COMPUTATION OF INVERSE OF A MATRIX BY ELEMENTARY TRANSFORMATION. THEOREMS ON RANK OF A MATRIX. Cayley Hamilton Theorem

    [...] Matrices | by VN Kala and Rajeshri Rana | 2009 | ISBN … [...]

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