Ch1 MATRICES AND VECTORS
1-1 Matrices and Matrix Operation
1-2 Matrix Inverse;Rules of Matrix Arithmetic
1-3 Norm(Length)and Dot Product
1-4 Cross Product
Ch2 GENERAL VECTOR SPACES
2-1 Real Vector Spaces
2-2 Subspaces
2-3 Linear Combination and Systems of Linear Equations
2-4 Linear Dependence and Linear Independence
2-5 Basis and Dimension
Ch3 LINEAR TRANSFORMATIONS
3-1 Linear Transformations
3-2 Range,Kernel,Rank and Nullity
3-3 Matrices of General Linear Transformations
3-4 Composition of Linear Transformation and Matrix Multiplication
3-5 Invertibillity and Isomorphisms
3-6 The Change of Coordinate Matrix
Ch4 ELEMENTARY MATRIX
4-1 Introduction to Systems of Linear Equations
4-2 Gaussian Elimination
4-3 Elementary Matrix and Elementary Operations
Ch5 DETERMINANTS
5-1 Definition of Determinant in Permutation(Option)
5-2 Determinants of 2*2 Matrix
5-3 Definition and Properties of the Determinant
5-4 Theorem Proof of Determinant
5-5 Cramer`s Rule
Ch6 INNER PRODUCT SPACES
6-1 Inner Product Space
6-2 Angle and Orthogonality in Inner Product Spaces
6-3 Orthonormal Bases;Gram-Schmidt Process;QR-Decomposition
6-4 Best Approximation:(Least Square Method)
6-5 Orthogonal Matrices
