Chap 1 Linear equations and matrix algebra

1-1 System of linear equations

1-2 Elimination

1-3 Elimination using matrix multiplications

1-4 Matrix algebra

1-5 Inverse matrices

1-6 Finding the inverse

1-7 LU factorization

1-8 Transposes

1-9 Block matrices

Chap 2 Vector spaces

2-1 Vector spaces and subspaces

2-2 Column space and nullspace

2-3 Reduced row echelon form

2-4 General solutions to Ax=b

2-5 Independence,basis and dimension

2-6 Four fundamental subspaces

2-7 Existence and uniqueness of inverses

Course Review 1（Chap1～2）

Chap 3 Linear transformations

3-1 Introduction to Linear transformations

3-2 Language of transformations

3-3 Coordinate systems and general vector spaces

3-4 Matrices of linear transformations

3-5 Change of basis

Chap 4 Orthogonality

4-1 Orthogonal vectors and orthogonal subspaces

4-2 Projections

4-3 Least squares approximations

4-4 Orthogonal matrices

4-5 Gram-Schmidt Process

Chap 5 Determinants

5-1 Properties of determinants

5-2 Formulas for deteminants

5-3 Applications of determinants

Course Review 2（Chap3～5）

Chap 6 Eigenanalysis

6-1 Eigenvalues and eigenvectors

6-2 Properties of eigenvalues and eigenvectors

6-3 Diagonalization

6-4 Difference equations

6-5 Differential equations

6-6 Complex eigenvalues

6-7 Similar matrices

Chap 7 Quadratic forms

7-1 Symmetric matrices

7-2 Introduction to quadratic forms

7-3 Positive definite matrices

7-4 Singular values

7-5 Singular value decomposition

Course Review 3（Chap6～7）

Review of Linear Algebra