Linear Algebra

Linear Algebra课程：前往报名学习

Linear Algebra视频慕课课程简介：

With the rapid development of information technology, the linear algebra course team has independently built a “procedural” learning platform, on which students can do exercises and tests by themselves. At the same time, by carrying out MOOC construction, the course is listed in the first group of National Quality Online Open Course in 2017.

前往报名学习

Linear Algebra课程列表：

Chapter 1 Determinants

-1.1.1 The 2nd and 3rd Order Determinants

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-1.1.2 The nth Order Determinants

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--Example

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-1.2.1 Cofactor Expansion Theorem and Transpose of Determinants

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--Example

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-1.2.2 Properties of Determinants

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-1.3.1 Evaluations of Determinants 1

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-1.3.2 Evaluations of Determinants 2

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-1.4.1 Cramer's Rule

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-1.4.2 Applications of Cramer's Rule

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--Homework

-Homework

Chapter 2 Matrix

-2.1.1 Matrix Operations

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--Video 2

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-2.1.2 Matrix Multiplication

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-2.2.1 The Transpose of a Matrix and Determinant of a Matrix

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-2.2.2 The Inverse of Matrix and Its Properties

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-2.3.1 The Calculation of Inverse Matrix

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-2.3.2 Partitioned Matrices and Their Operations

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--Video 2

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-2.4.1 Elementary Operations and Elementary Matrices

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--Video 2

--Video 3

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-2.4.2 Application of Elementary Operations and Elementary Matrices

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-Homework

Chapter 3 Linear Dependence of Vector Set

-3.1.1 Vectors and its Operations

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-3.1.2 Linear Combination

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-3.2.1 Linear Dependence

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--Video 2

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-3.2.2 Determination of Linear Dependence

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-3.3.1 Maximum Independent Subset

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-3.3.2 Rank of Vector Set

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-3.4.1 Rank of Matrix

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-3.4.2 Method for Finding the Rank of Matrix and Vector Set

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-Homework

Mid-term Examination

-Test

Chapter 4 Linear Equations and Linear Spaces

-4.1.1 Decision of Solutions to Linear System

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-4.1.2 Elimination Method for Solving Linear System

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-4.1.3 Decision theorem of solution

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-4.2.1 Structure of Solutions to Homogeneous System

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-4.2.2 Structure of Solutions to Nonhomogeneous System

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-4.3.1 Linear Space

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-4.3.2 Subspaces

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-4.4.1 Basis and Dimension

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-4.4.2 Coordinate Vector and Isomorphic Vector Spaces

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-4.4.3 Change of Basis and Change of Coordinate

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-4.5 Linear Transformation

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--Vedio 2

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-4.6 Euclidean Space

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-Homework

Chapter 5 Eigenvalues and Eigenvectors

-5.1.1 Eigenvalues and Eigenvectors

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-5.1.2 Properties of Eigenvalues and Eigenvectors

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-5.2.1 Similar Matrices

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-5.2.2 Diagonalization and its Conditions

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-5.3 Real Symmtric Matrices and its Orthogonal Similar Diagonalization

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Chapter 6 Quadratic Forms

-6.1.1 Quadratic Forms and Their Standard Forms

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--Video 2

--Video 3

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-6.1.2 Using Orthogonal Transformations to Deduce the Quadratic Forms to the Standard Forms

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-6.2.1 Using the Method of Completing Squares to Reduce the Quadratic Forms to the Standard Forms

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-6.2.2 Positive Definite Quadratic Forms

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--Video 2

--Video 3

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--Homework

-Homework

Final Examination

-Test

Linear Algebra开设学校：东北大学

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