Linear Algebra with Applications

Linear Algebra with Applications课程：前往报名学习

Linear Algebra with Applications视频慕课课程简介：

This course "Linear Algebra with Applications" covers a comprehensive and systematic basic theory of linear algebra, and some practical applications in our social life and scientific research nowadays. The teacher has more than ten years of teaching experience of this course using English, and the members/assistant of our team also have rich teaching experience. Welcome to join our course "Linear Algebra with Applications" of Beijing Jiaotong University! Enjoy the beauty of Linear Algebra!

前往报名学习

Linear Algebra with Applications课程列表：

Chapter 1 - Matrices and Systems of Equations

-1.1 Systems of Linear Equations

--1.1-1 The Form, Solution and 2-by-2 System

--1.1-2 Equivalent Systems

--1.1-3 n-by-n Systems

-1.2 Row Echelon Form

--1.2-1 Row Echelon Form and Gaussian Elimination

--1.2-2 Overdetermined System and Undetermined System

--1.2-3 Reduced Row Echelon Form

--1.2-4 Applications

-1.3 Matrix Algebra

--1.3-1 Matrix Notation, Vectors and Equality

--1.3-2 Matrix Addition, Scalar Multiplication, Matrix Multiplication and Linear System

--1.3-3 Transpose of a Matrix, and Symmetric Matrix

--1.3-4 Algebraic Rules

--1.3-5 Identity Matrix, and Inverse Matrix

-1.4 Elementary matrices

--1.4-1 Equivalent Systems and Elementary Matrices

--1.4-2 Equivalent Systems and Equivalent Conditions

--1.4-3 Triangular Factorization

-1.5 Partitioned Matrices

--1.5 Partitioned Matrices

-Homewrok 1

-Test 1

Chapter 2 - Determinants

-2.1 Determinant

--2.1-1 Motivation

--2.1-2 Determinants and Properties

-2.2 Properties of Determinant

--2.2-1 Lemma 2.2.1

--2.2-2 Determinants and Properties

--2.2-3 Singularity and Determinant

-2.3 Additional Topics and Applications

--2.3-1 The Adjoint of a Matrix

--2.3-2 Cramer’s Rule and Cross Product

-Homework 2

-Test 2

Chapter 3 Vector Spaces

-3.1 Definition and Examples

--3.1-1 Simple Examples of Vector Spaces

--3.1-2 Vector Spaces, More Examples and Properties

-3.2 Subspaces

--3.2-1 Subspace and Examples

--3.2-2 Span and Spanning Set

-3.3 Linear Independence

--3.3-1 Minimal Spanning Set

--3.3-2 Linear Independence and Dependence

--3.3-3 Linear Dependence and Singularity

--3.3-4 Linear Independence and Dependence in Pn and C(n-1)[a,b]

-3.4 Basis and Dimension

--3.4-1 Basis

--3.4-2 Dimension

-3.5 Change of Basis

--3.5 Change of Basis

-3.6 Row Space and Column Space

--3.6-1 Definition

--3.6-2 Linear System

--3.6-3 The Column Space

-Homework 3

-Test 3

Chapter 4 Linear Transformations

-4.1 Definition and Examples

--4.1-1 Definition and Simple Examples

--4.1-2 The Image and Kernel

-4.2 Matrix Representation of Linear Transformations

--4.2-1 Matrix Representation of L form Rn to Rm

--4.2-2 Matrix Representation of L from V to W

--4.2-3 Matrix Form of LA from Rn to Rm

-4.3 Similarity

--4.3-1 Matrix Representation of a Linear Operator

-Homework 4

-Test 4

Chapter 5 Orthogonality

-5.1 The Scalar Product in Rn

--5.1-1 The Scalar Product in R2 and R3

--5.1-2 Scalar and Vector Projections; Orthogonality in Rn

-5.2 Orthogonal Subspaces

--5.2-1 Orthogonal Subspaces; Orthogonal Complement

--5.2-2 Fundamental Subspaces

-5.3 Least Squares Problems

--5.3-1 Least Squares Solutions to Overdetermined Systems

--5.3-2 Examples

-5.6 The Gram-Schimidt Orthogonalization Process

--5.6-1 Preliminaries

--5.6-2 The Gram-Schimidt Orthogonalization Process

--5.6-3 The Gram-Schimidt QR Factorization

-Homewrok 5

-Test 5

Chapter 6 Eigenvalues

-6.1 Eigenvalues and Eigenvectors

--6.1-1 Definition and Calculation of Eigenvalues and Eigenvectors

--6.1-2 Product and Sum of Eigenvalues

-6.3 Diagonalization

--6.3-1 Diagonalizable Matrices

--6.3-2 Examples

-6.6 Quadratic Forms

--6.6-1 Conic Sections

--6.6-2 Quadratic Surface

-6.7 Positive Definite Matrices

--6.7 Positive Definite Matrices

-Homework 6

-Test 6

Linear Algebra with Applications开设学校：北京交通大学

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