Dimension、Rank、The Fundamental Theorem of Invertible Matrices

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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

目前顯示第 1 至第 50 個資料列，總計 112 個資料列