Linear or Nonlinear Equation、A system of Linear Equation in R^2 and R^3、Coefficient and Augmented Metrices

Homepage » ALL COURSE » College of Science » Department of Electrophysics » Applied Maths-Linear Algebra, Vector Analysis – 106 Academic Year | Department of Electrophysics Prof. Wen-Bin Jian » Linear or Nonlinear Equation、A system of Linear Equation in R^2 and R^3、Coefficient and Augmented Metrices

Linear or Nonlinear Equation、A system of Linear Equation in R^2 and R^3、Coefficient and Augmented Metrices

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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

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