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Chapter 1 Matrices and Determinants
1£®1 Matrices
1£®2 Matrix Arithmetic
1£®2£®1 Equality
1£®2£®2 Scalar Multiplication
1£®2£®3 Matrix Addition
1£®2£®4 Matrix Multiplication
1£®2£®5 Transpose of a Matrix
1£®3 Determinants of Square Matrices
1£®3£®1 Second Order Determinant
1£®3£®2 n-th Order Determinant
1£®3£®3 Properties of Determinants
1£®3£®4 Evaluation of Determinants
1£®3£®5 Laplace's Theorem
1£®4 Block Matrices
1£®4£®1 The Concept of Block Matrices
1£®4£®2 Evaluation of Block Matrices
1£®5 Invertible Matrices
1£®6 Elementary Matrices
1£®6£®1 Elementary Operations of Matrices
1£®6£®2 Elementary Matrices
1£®6£®3 Use Elementary Operations to Get the Inverse Matrix
1£®7 Rank of Matrices
1£®8 Exercises

Chapter 2 Systems of Linear Equations
2£®1 Systems of Linear Equations
2£®2 Vectors
2£®3 Linear Independence
2£®3£®1 Linear Combination
2£®3£®2 Linear Dependence and Linear Independence
2£®4 Maximally Linearly Independent Vector Group
2£®4£®1 Equivalent Vector Sets
2£®4£®2 Maximally Linearly Independent Group
2£®4£®3 The Relationship Between Rank of Matrices and Rank of Vector Sets
2£®5 Vector Space
2£®6 General Solutions of Linear Systems
2£®6£®1 General Solutions of Homogenous Linear Systems
2£®6£®2 General Solutions of Non-homogenous Linear Systems
2£®7 Exercises

Chapter 3 Eigenvalues and Eigenveetors
3£®1 Eigenvalues and Eigenvectors
3£®1£®1 Definition of Eigenvalues and Eigenvectors
3£®1£®2 Properties of Eigenvalues and Eigenvectors
3£®2 Diagonalization o{ Square Matrices
3£®2£®1 Similar Matrix
3£®2£®2 Diagonalization of Square Matrices
3£®3 Orthonormal Basis
3£®3£®1 Inner Product of Vectors
3£®3£®2 Orthogonal Set and Basis
3£®3£®3 Gram-Schmidt Orthogonalization Process
3£®3£®4 Orthogonal Matrix
3£®4 Diagonalization of Real Symmetric Matrices
3£®4£®1 Properties of Eigenvalues of Real Symmetric Matrices
3£®5 Exercises

Chapter 4 Quadratic Form
4£®1 Real Quadratic Form and Its Matrix
4£®2 Diagonal Form of Quadratic Form
4£®3 Diagonal Form of Real Quadratic Form
4£®3£®1 Changing Quadratic Form into Diagonal Form by Orthogonal Transformation
4£®3£®2 Changing Quadratic Form into Diagonal Form by the Method of Completing the Square
4£®4 Canonical Form of Real Quadratic Form
4£®5 Positive Definite Quadratic Form and Matrices
4£®6 Exercises
References