Orthogonal Diagonalizable
| 週次 | 課程內容 | 課程影音 |
|---|---|---|
| 第一週 | Cartesian Plane、Vector in The Cartesian Plane、Vector Addition | 線上觀看 |
| Vector Addition、Vector in R^3 and R^n、Algebraic Properties of Vector in R^n and Proof | 線上觀看 | |
| Using Algebraic Properties for computation、Independent Vector Spanning R^2 Space、Linear Combination、Binary Vector | 線上觀看 | |
| Dot Product、Definition and Example、Algebraic Properties of Dot Product | 線上觀看 | |
| Length、Unit Vector、The Cauchy-Schwartz and Triangle Inequality、Distance between Two Vector | 線上觀看 | |
| Angle between Two Vectors、Angle and Orthogonal Property、Dot Operation and Orthogonality of Function、Pythagoras’ Theorem and Projection | 線上觀看 | |
| Lines in R^2 and R^3 | 線上觀看 | |
| Lines in R^2 and R^3、Planes in R^3 | 線上觀看 | |
| Distance from a Point to a Line/Plane、Applications | 線上觀看 | |
| 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 |
| Row Echelon Form、Elementary Row Operation and Row Equivalent、Gaussian Elimination | 線上觀看 | |
| Rank and Gaussian-Jordan Elimination、Gaussian-Jordan Elimination、Homogeneous Systems、Linear Systems over Z_p | 線上觀看 | |
| Vector Concepts for Linear Combinations、Spanning Set for Space R^n | 線上觀看 | |
| Spanning Set for Space R^n、Linear independence | 線上觀看 | |
| Linear independence | 線上觀看 | |
| Application(Chemical、Network Analysis) | 線上觀看 | |
| Application(Circuit、Economic Models) | 線上觀看 | |
| Application(Finite Linear Games)、Numerical Solutions-Iterative Methods | 線上觀看 | |
| 第三週 | Introduction to Matrix Operations、Matrix Operations、Matrix’s Equality | 線上觀看 |
| Matrix Addition and Scalar Multiplication、Matrix Multiplication、Partitioned Matrices | 線上觀看 | |
| Partitioned Matrices、Matrix Power、The Transpose of a Matrix | 線上觀看 | |
| Properties of Addition and Scalar Multiplication、Properties of Matrix Multiplication | 線上觀看 | |
| Properties of The Transpose、The inverse of a Matrix | 線上觀看 | |
| Properties of Invertible Matrices、Elementary Matrices | 線上觀看 | |
| The Fundamental Theorem of Invertible Matrices、The Gaussian-Jordan Method for Computing The Inverse | 線上觀看 | |
| The Gaussian-Jordan Method for Computing The Inverse、The LU Factorization | 線上觀看 | |
| An Easy Way to Find LU Factorizations、The P^TLU Factorization、Computational Consideration | 線上觀看 | |
| 第四週 | Subspace、Row and Column Space of Matrice(Introduction) | 線上觀看 |
| Row and Column Space of Matrice、Basis and Effective Procedures to Find Basis | 線上觀看 | |
| Dimension、Rank、The Fundamental Theorem of Invertible Matrices | 線上觀看 | |
| Introduction to Linear Transformations、Linear Transformations | 線上觀看 | |
| Linear Transformations、Rotation About The Origin、Composition of Two Transformations | 線上觀看 | |
| Composition of Two Transformations、Inverse of Linear Transformations、Associativity | 線上觀看 | |
| Introduction to Markov Chain、Markov Chain-State Vector、Transition Matrix and Steady State Vector | 線上觀看 | |
| Application Example of Markov Chain、Linear Economic Model-Leontief Model、Productive、Population Growth-Leslie Model | 線上觀看 | |
| Population Growth-Leslie Model、Graph、Digraph | 線上觀看 | |
| Digraph、Error-Correction Codes | 線上觀看 | |
| 第五週 | Introduction to Eigenvalues and Eigenvectors、Eigenspace | 線上觀看 |
| Eigenspace、Eigenpicture | 線上觀看 | |
| Eigenpicture-Zero Determinant、Calculate Eigenvalues | 線上觀看 | |
| Concept of Determinant and How to calculate、Determinant of n×n matrices、The Laplace Expansion | 線上觀看 | |
| The Examples of Laplace Expansion、Properties of Determinants | 線上觀看 | |
| Determinants of Elementary Matrices、Determinants and Matrix Operations、Cramer’s Rule and The Adjoint | 線上觀看 | |
| Eigenvalues of a Square Matrix | 線上觀看 | |
| Eigenvalues of a Square Matrix、The Fundamental Theorem of Invertible Matrices | 線上觀看 | |
| Polynomial of a matrix A and Its corresponding eigenvalues | 線上觀看 | |
| 第七週 | Similar Matrices | 線上觀看 |
| Diagonalization | 線上觀看 | |
| Diagonalization、The Diagonalization Theorem | 線上觀看 | |
| The Power Method | 線上觀看 | |
| The Power Method、The Shifted Power Method、The Inverse Power Method | 線上觀看 | |
| The Shifted Inverse Power Method、Gerschgorin’s Theorem | 線上觀看 | |
| Markov Chains | 線上觀看 | |
| Population Growth、Leslie matrix、Perron-Frobenius Theorem | 線上觀看 | |
| Linear Recurrence Relation | 線上觀看 | |
| System of Linear Differential Equations | 線上觀看 | |
| Exponential of A - e^A、Discrete Linear Dynamical Systems | 線上觀看 | |
| Discrete Linear Dynamical Systems | 線上觀看 | |
| 第八週 | Orthogonal Sets of Vectors、Coordinate | 線上觀看 |
| Orthogonal Matrices、Orthogonal Complements | 線上觀看 | |
| Orthogonal Projections、Orthogonal Decompositions | 線上觀看 | |
| The Gram-Schmidt Process、QR Factorization | 線上觀看 | |
| Orthogonal Diagonalizable | 線上觀看 | |
| Spectral Theorem | 線上觀看 | |
| Dual Codes-The generated Code Space C、Dual Codes-The Same or Equivalent Code | 線上觀看 | |
| Quadratic Forms、Quadratic Forms-diagonalization and Principle Axes Theorem | 線上觀看 | |
| Quadratic Forms、Definition and Example、Diagonalization and Principal Axes Theorem | 線上觀看 | |
| The Fundamental Theorem of Quadratic Forms | 線上觀看 | |
| Graphing Quadratic Equations、Identify and graph the conic | 線上觀看 | |
| Graphing Quadratic Equations、Identify the quadric surface of the equation | 線上觀看 | |
| 第九週 | Vector Space、Examples of Kinds of Vector Space | 線上觀看 |
| Examples of Vector or Non-Vector Space、Zero and Negative vector、Subspace | 線上觀看 | |
| Spanning Set | 線上觀看 | |
| Linear Independence、 Bases | 線上觀看 | |
| Coordinate | 線上觀看 | |
| Dimension | 線上觀看 | |
| Change-of-Basis Matrices | 線上觀看 | |
| The Gauss-Jordan Method for Computing a change-of-Basis Matrix | 線上觀看 | |
| 第十週 | Linear Transformations、Definition and Example | 線上觀看 |
| Properties of Linear Transformations,、Composition of Linear Transformations, Inverse of Linear Transformation | 線上觀看 | |
| The Kernel and Range of a Linear Transformations、Definition and Example | 線上觀看 | |
| The Kernel and Range of a Linear Transformations、The Rank Theorem、One-to-One and Onto Linear Transformations | 線上觀看 | |
| The Kernel and Range of a Linear Transformations、The Rank Theorem、One-to-One and Onto Linear Transformations | 線上觀看 | |
| Linear Transformations Represented by a Matrix | 線上觀看 | |
| Matrices of Composite and Inverse Linear Transformations | 線上觀看 | |
| Change of Basis and Similarity | 線上觀看 | |
| The Fundamental Theorem of Invertible Matrices | 線上觀看 | |
| 1st Order Homogeneous,Linear,Differential,Equations、2nd Order Homogeneous,Linear,Differential,Equations | 線上觀看 | |
| 第十一週 | Extends from 1D to 3D Vector Space、Scalar Functions , Functions of Scalar of Functions of Vector、Vector Functions of Vector | 線上觀看 |
| Vector-Function Curve,3D to 1D Vsinf Parameter 、Find the Intersection Curve 、Limits of a Vector Functions 、Continuity and Derivative of Vector Function | 線上觀看 | |
| Calculate the tangent line of a curve、Differentiation and Integration of the Curve、 The length of a Curve、The Arc length Parameter | 線上觀看 | |
| Trajectory of a particle | 線上觀看 | |
| Calculation of Curvature | 線上觀看 | |
| Normal and Binormal Vectors、Tangent, Normal and Binormal Vectors、Another Method for the Calculation of Curvature、Curvature of Twisted Cubic | 線上觀看 | |
| Level Curves for Functions of two variables、Functions of three variables F(x,y,z)、 Partial Derivatives of Functions | 線上觀看 | |
| Scalar Functions to Vector Functions、Gradient Calculation | 線上觀看 | |
| Concept of Gradient Calculation、Gradient Calculation | 線上觀看 | |
| 第十三週 | Level Curves and Gradient | 線上觀看 |
| Vector fields,The del operator | 線上觀看 | |
| Concept of Divergence Calculation、Curl less or Divergent less Potential、Scalar or Vector Potential | 線上觀看 | |
| Line Integrals on a 2D plane | 線上觀看 | |
| Line Integrals on a 2D plane | 線上觀看 | |
| Line Integrals on a 2D plane-Plane Work done by force | 線上觀看 | |
| Path Independence Integration Result、Conservative Vector Fields | 線上觀看 | |
| Conservative Vector Fields | 線上觀看 | |
| Test for a Conservative Vector field | 線上觀看 | |
| 第十四週 | Introduction to Double Integrals、Applications of Double Integrals | 線上觀看 |
| Calculation of Double Integrals、Change of Variables、Double Integrals in Poar coordinates | 線上觀看 | |
| Change of variables | 線上觀看 | |
| Proof of Green’s Theorem | 線上觀看 | |
| Green’s Theorem and Calculation 、Stoke’s Theorem、Application of Green’s Theorem | 線上觀看 | |
| Application of Green’s Theorem、Apply Green’s Theorem in the region with holes | 線上觀看 |
課程專區
選單