週次 | 課程內容 | 課程影音 | 課程下載 |
---|---|---|---|
第一週 | Cartesian Plane、Vector in The Cartesian Plane、Vector Addition | 線上觀看 | MP4下載 |
Vector Addition、Vector in R^3 and R^n、Algebraic Properties of Vector in R^n and Proof | 線上觀看 | MP4下載 | |
Using Algebraic Properties for computation、Independent Vector Spanning R^2 Space、Linear Combination、Binary Vector | 線上觀看 | MP4下載 | |
Dot Product、Definition and Example、Algebraic Properties of Dot Product | 線上觀看 | MP4下載 | |
Length、Unit Vector、The Cauchy-Schwartz and Triangle Inequality、Distance between Two Vector | 線上觀看 | MP4下載 | |
Angle between Two Vectors、Angle and Orthogonal Property、Dot Operation and Orthogonality of Function、Pythagoras’ Theorem and Projection | 線上觀看 | MP4下載 | |
Lines in R^2 and R^3 | 線上觀看 | MP4下載 | |
Lines in R^2 and R^3、Planes in R^3 | 線上觀看 | MP4下載 | |
Distance from a Point to a Line/Plane、Applications | 線上觀看 | MP4下載 | |
第二週 | Linear or Nonlinear Equation、A system of Linear Equation in R^2 and R^3、Coefficient and Augmented Metrices | 線上觀看 | MP4下載 |
Row Echelon Form、Elementary Row Operation and Row Equivalent、Gaussian Elimination | 線上觀看 | MP4下載 | |
Rank and Gaussian-Jordan Elimination、Gaussian-Jordan Elimination、Homogeneous Systems、Linear Systems over Z_p | 線上觀看 | MP4下載 | |
Vector Concepts for Linear Combinations、Spanning Set for Space R^n | 線上觀看 | MP4下載 | |
Spanning Set for Space R^n、Linear independence | 線上觀看 | MP4下載 | |
Linear independence | 線上觀看 | MP4下載 | |
Application(Chemical、Network Analysis) | 線上觀看 | MP4下載 | |
Application(Circuit、Economic Models) | 線上觀看 | MP4下載 | |
Application(Finite Linear Games)、Numerical Solutions-Iterative Methods | 線上觀看 | MP4下載 | |
第三週 | Introduction to Matrix Operations、Matrix Operations、Matrix’s Equality | 線上觀看 | MP4下載 |
Matrix Addition and Scalar Multiplication、Matrix Multiplication、Partitioned Matrices | 線上觀看 | MP4下載 | |
Partitioned Matrices、Matrix Power、The Transpose of a Matrix | 線上觀看 | MP4下載 | |
Properties of Addition and Scalar Multiplication、Properties of Matrix Multiplication | 線上觀看 | MP4下載 | |
Properties of The Transpose、The inverse of a Matrix | 線上觀看 | MP4下載 | |
Properties of Invertible Matrices、Elementary Matrices | 線上觀看 | MP4下載 | |
The Fundamental Theorem of Invertible Matrices、The Gaussian-Jordan Method for Computing The Inverse | 線上觀看 | MP4下載 | |
The Gaussian-Jordan Method for Computing The Inverse、The LU Factorization | 線上觀看 | MP4下載 | |
An Easy Way to Find LU Factorizations、The P^TLU Factorization、Computational Consideration | 線上觀看 | MP4下載 | |
第四週 | Subspace、Row and Column Space of Matrice(Introduction) | 線上觀看 | MP4下載 |
Row and Column Space of Matrice、Basis and Effective Procedures to Find Basis | 線上觀看 | MP4下載 | |
Dimension、Rank、The Fundamental Theorem of Invertible Matrices | 線上觀看 | MP4下載 | |
Introduction to Linear Transformations、Linear Transformations | 線上觀看 | MP4下載 | |
Linear Transformations、Rotation About The Origin、Composition of Two Transformations | 線上觀看 | MP4下載 | |
Composition of Two Transformations、Inverse of Linear Transformations、Associativity | 線上觀看 | MP4下載 | |
Introduction to Markov Chain、Markov Chain-State Vector、Transition Matrix and Steady State Vector | 線上觀看 | MP4下載 | |
Application Example of Markov Chain、Linear Economic Model-Leontief Model、Productive、Population Growth-Leslie Model | 線上觀看 | MP4下載 | |
Population Growth-Leslie Model、Graph、Digraph | 線上觀看 | MP4下載 | |
Digraph、Error-Correction Codes | 線上觀看 | MP4下載 | |
第五週 | Introduction to Eigenvalues and Eigenvectors、Eigenspace | 線上觀看 | MP4下載 |
Eigenspace、Eigenpicture | 線上觀看 | MP4下載 | |
Eigenpicture-Zero Determinant、Calculate Eigenvalues | 線上觀看 | MP4下載 | |
Concept of Determinant and How to calculate、Determinant of n×n matrices、The Laplace Expansion | 線上觀看 | MP4下載 | |
The Examples of Laplace Expansion、Properties of Determinants | 線上觀看 | MP4下載 | |
Determinants of Elementary Matrices、Determinants and Matrix Operations、Cramer’s Rule and The Adjoint | 線上觀看 | MP4下載 | |
Eigenvalues of a Square Matrix | 線上觀看 | MP4下載 | |
Eigenvalues of a Square Matrix、The Fundamental Theorem of Invertible Matrices | 線上觀看 | MP4下載 | |
Polynomial of a matrix A and Its corresponding eigenvalues | 線上觀看 | MP4下載 | |
第七週 | Similar Matrices | 線上觀看 | MP4下載 |
Diagonalization | 線上觀看 | MP4下載 | |
Diagonalization、The Diagonalization Theorem | 線上觀看 | MP4下載 | |
The Power Method | 線上觀看 | MP4下載 |