5.6-1 Preliminaries在线视频

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

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