دانلود کتاب Linear Algebra

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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
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