1.1-Linear Systems

1.2-Gauss method

1.3-Iterative equation-solving methods

2.1-Matrices

2.2-Matrix Algebraic Properties

2.3-Determinants

2.4-Evaluating Determinants

2.5-combinatorial definition of determinants

2.6-Elementary Matrices and Invertible Matrices

2.7-Properties of determinants

2.8-LU-Decomposition

3.1-Vector space

3.2-Subspace

3.3-Linear independence

3.4-Basis and dimension

3.5-Row space and column space

3.6-Null Space

4.1-Inner product

4.2-Norm and angle

4.3-Orthogonality

4.4-Orthonormal basis

4.5-Gram-Schmidt process

4.6-QR-decomposition

4.7-Best approximation and least squares

4.8-Least Square Data Fitting

4.9-Application to correlation

5.1-Eigenvectors and eigenvalue

5.2-Diagonalization

5.3-Application To Discrete Dynamical Systems

5.4-Application to differential equations

5.5-Iterative estimates for eigenvalues

6.1-Orthogonal matrices

6.2-Orthogonal Diagonalization

6.3-Quadratic forms