Week | Course Content | Course Video | Course Download |
---|---|---|---|
Week 1 | Cartesian Plane、Vector in The Cartesian Plane、Vector Addition | Watch Online | MP4 Download |
Vector Addition、Vector in R^3 and R^n、Algebraic Properties of Vector in R^n and Proof | Watch Online | MP4 Download | |
Using Algebraic Properties for computation、Independent Vector Spanning R^2 Space、Linear Combination、Binary Vector | Watch Online | MP4 Download | |
Dot Product、Definition and Example、Algebraic Properties of Dot Product | Watch Online | MP4 Download | |
Length、Unit Vector、The Cauchy-Schwartz and Triangle Inequality、Distance between Two Vector | Watch Online | MP4 Download | |
Angle between Two Vectors、Angle and Orthogonal Property、Dot Operation and Orthogonality of Function、Pythagoras’ Theorem and Projection | Watch Online | MP4 Download | |
Lines in R^2 and R^3 | Watch Online | MP4 Download | |
Lines in R^2 and R^3、Planes in R^3 | Watch Online | MP4 Download | |
Distance from a Point to a Line/Plane、Applications | Watch Online | MP4 Download | |
Week 2 | Linear or Nonlinear Equation、A system of Linear Equation in R^2 and R^3、Coefficient and Augmented Metrices | Watch Online | MP4 Download |
Row Echelon Form、Elementary Row Operation and Row Equivalent、Gaussian Elimination | Watch Online | MP4 Download | |
Rank and Gaussian-Jordan Elimination、Gaussian-Jordan Elimination、Homogeneous Systems、Linear Systems over Z_p | Watch Online | MP4 Download | |
Vector Concepts for Linear Combinations、Spanning Set for Space R^n | Watch Online | MP4 Download | |
Spanning Set for Space R^n、Linear independence | Watch Online | MP4 Download | |
Linear independence | Watch Online | MP4 Download | |
Application(Chemical、Network Analysis) | Watch Online | MP4 Download | |
Application(Circuit、Economic Models) | Watch Online | MP4 Download | |
Application(Finite Linear Games)、Numerical Solutions-Iterative Methods | Watch Online | MP4 Download | |
Week 3 | Introduction to Matrix Operations、Matrix Operations、Matrix’s Equality | Watch Online | MP4 Download |
Matrix Addition and Scalar Multiplication、Matrix Multiplication、Partitioned Matrices | Watch Online | MP4 Download | |
Partitioned Matrices、Matrix Power、The Transpose of a Matrix | Watch Online | MP4 Download | |
Properties of Addition and Scalar Multiplication、Properties of Matrix Multiplication | Watch Online | MP4 Download | |
Properties of The Transpose、The inverse of a Matrix | Watch Online | MP4 Download | |
Properties of Invertible Matrices、Elementary Matrices | Watch Online | MP4 Download | |
The Fundamental Theorem of Invertible Matrices、The Gaussian-Jordan Method for Computing The Inverse | Watch Online | MP4 Download | |
The Gaussian-Jordan Method for Computing The Inverse、The LU Factorization | Watch Online | MP4 Download | |
An Easy Way to Find LU Factorizations、The P^TLU Factorization、Computational Consideration | Watch Online | MP4 Download | |
Week 4 | Subspace、Row and Column Space of Matrice(Introduction) | Watch Online | MP4 Download |
Row and Column Space of Matrice、Basis and Effective Procedures to Find Basis | Watch Online | MP4 Download | |
Dimension、Rank、The Fundamental Theorem of Invertible Matrices | Watch Online | MP4 Download | |
Introduction to Linear Transformations、Linear Transformations | Watch Online | MP4 Download | |
Linear Transformations、Rotation About The Origin、Composition of Two Transformations | Watch Online | MP4 Download | |
Composition of Two Transformations、Inverse of Linear Transformations、Associativity | Watch Online | MP4 Download | |
Introduction to Markov Chain、Markov Chain-State Vector、Transition Matrix and Steady State Vector | Watch Online | MP4 Download | |
Application Example of Markov Chain、Linear Economic Model-Leontief Model、Productive、Population Growth-Leslie Model | Watch Online | MP4 Download | |
Population Growth-Leslie Model、Graph、Digraph | Watch Online | MP4 Download | |
Digraph、Error-Correction Codes | Watch Online | MP4 Download | |
Week 5 | Introduction to Eigenvalues and Eigenvectors、Eigenspace | Watch Online | MP4 Download |
Eigenspace、Eigenpicture | Watch Online | MP4 Download | |
Eigenpicture-Zero Determinant、Calculate Eigenvalues | Watch Online | MP4 Download | |
Concept of Determinant and How to calculate、Determinant of n×n matrices、The Laplace Expansion | Watch Online | MP4 Download | |
The Examples of Laplace Expansion、Properties of Determinants | Watch Online | MP4 Download | |
Determinants of Elementary Matrices、Determinants and Matrix Operations、Cramer’s Rule and The Adjoint | Watch Online | MP4 Download | |
Eigenvalues of a Square Matrix | Watch Online | MP4 Download | |
Eigenvalues of a Square Matrix、The Fundamental Theorem of Invertible Matrices | Watch Online | MP4 Download | |
Polynomial of a matrix A and Its corresponding eigenvalues | Watch Online | MP4 Download | |
Week 7 | Similar Matrices | Watch Online | MP4 Download |
Diagonalization | Watch Online | MP4 Download | |
Diagonalization、The Diagonalization Theorem | Watch Online | MP4 Download | |
The Power Method | Watch Online | MP4 Download |