Chapter 1 System of Linear Equatio and Elimination Method 1.1 Solving System of Linear Equatio with Elimination Method 1.1.1 Linear System with Two Unknow 1.1.2 Gauss-Jordan Elimination Method 1.2 Applicatio Practice 1Chapter 2 Matrices 2.1 Basic Concepts 2.1.1 Matrices 2.1.2 Special Matrices 2.1.3 Problems Related to Matrices 2.2 Basic Operatio 2.2.1 Definitio 2.2.2 Rules of Operatio 2.2.3 Applicatio 2.3 Matrix Invees 2.3.1 Invertible Matrices 2.3.2 Orthogonal Matrices 2.4 Blocks and Sub-matrices 2.4.1 Block Operatio 2.4.2 Column Blocks 2.4.3 Sub-matrices 2.5 Elementary Operatio and Elementary Matrices 2.5.1 Definitio and Properties 2.5.2 Equivalent Normal Form for Matrices 2.5.3 Invertible Matrices Revisit 2.5.4 Unique solution for n×n linear systems 2.6 Applicatio(Input-output Analysis) Practice 2Chapter 3 Determinants 3.1 Definitio and Properties of Determinants 3.1.1 Definitio 3.1.2 Properties 3.2 Evaluation of Determinants 3.3 Applicatio 3.3.1 Adjugate Matriees and Invee Formula 3.3.2 Cramer's Rule 3.3.3 Summary Praetiee 3Chapter 4 Rank of a Matrix and Solutio for Linear Systen 4.1 Rank of a Matrix. 4.1.1 Concepts 4.1.2 Computatio 4.2 Solutio of Linear Systems 4.2.l Homogeneous Systems 4.2.2 Non-homogeneous Systems Practice 4Chapter 5 Vector Spaces 5.1 Concepts 5.2 Linear Dependence and Linear Independence 5.2.1 Coneepts 5.2.2 Properties 5.2.3 Rank of a Set of Veeto 5.2.4 Row and Column Ranks of a Matrix 5.3 Bases and Dimeio of Vector Spaces 5.3.1 Bases and Dimeio 5.3.2 Revisit Solutio for Linear Systems 5.4 Inner Products 5.4.1 Review 5.4.2 Inner Produets and Orthogonal Matrices(158) 5.4.3 Four Basle Subspaees(163) Practice 5Chapter 6 Eigenvalues 6.1 Eigenvalues and Eigenvecto 6.2 Diagonalizatio' 6.2.1 Similar Matriees and Diagonal Forms(172) 6.2.2 Applieatio ( 178 ) 6.3 Real Symmetric Matrices and Quadratic Forms 6.3.1 Canonical Forms for Real Symmetric Matrices 6.3.2 Quadratic Forms 6.3.3 Quadratic Expressio and Their Canonical Forms 6.4 Positive Definite Matrices and Classification of QuadraticForms 6.4.1 Positive Definite Matrices 6.4.2 Optimization 6.4.3 Generalized Eigenvalue Problems Practice 6Chapter 7 Linear Traformatio 7.1 Basic Concepts of Linear Traformatio 7.1.1 Linear Traformatio 7.1.2 Range and Kernel for a Linear Traformation 7.2 Linear Traformatio and Matrices 7.2.1 Coordinate Vecto 7.2.2 The Matrix Representatio for Linear Traformatio 7.2.3 Engenvalues and Eigenvecto of a Linear Traformation Practice 7References
Chapter 1 System of Linear Equatio and Elimination Method 1.1 Solving System of Linear Equatio with Elimination Method 1.1.1 Linear System with Two Unknow 1.1.2 Gauss-Jordan Elimination Method 1.2 Applicatio Practice 1 Chapter 2 Matrices 2.1 Basic Concepts 2.1.1 Matrices 2.1.2 Special Matrices 2.1.3 Problems Related to Matrices 2.2 Basic Operatio 2.2.1 Definitio 2.2.2 Rules of Operatio 2.2.3 Applicatio 2.3 Matrix Invees 2.3.1 Invertible Matrices 2.3.2 Orthogonal Matrices 2.4 Blocks and Sub-matrices 2.4.1 Block Operatio 2.4.2 Column Blocks 2.4.3 Sub-matrices 2.5 Elementary Operatio and Elementary Matrices 2.5.1 Definitio and Properties 2.5.2 Equivalent Normal Form for Matrices 2.5.3 Invertible Matrices Revisit 2.5.4 Unique solution for n×n linear systems 2.6 Applicatio(Input-output Analysis) Practice 2 Chapter 3 Determinants 3.1 Definitio and Properties of Determinants 3.1.1 Definitio 3.1.2 Properties 3.2 Evaluation of Determinants 3.3 Applicatio 3.3.1 Adjugate Matriees and Invee Formula 3.3.2 Cramer's Rule 3.3.3 Summary Praetiee 3 Chapter 4 Rank of a Matrix and Solutio for Linear Systen 4.1 Rank of a Matrix . 4.1.1 Concepts 4.1.2 Computatio 4.2 Solutio of Linear Systems 4.2.l Homogeneous Systems 4.2.2 Non-homogeneous Systems Practice 4 Chapter 5 Vector Spaces 5.1 Concepts 5.2 Linear Dependence and Linear Independence 5.2.1 Coneepts 5.2.2 Properties 5.2.3 Rank of a Set of Veeto 5.2.4 Row and Column Ranks of a Matrix 5.3 Bases and Dimeio of Vector Spaces 5.3.1 Bases and Dimeio 5.3.2 Revisit Solutio for Linear Systems 5.4 Inner Products 5.4.1 Review 5.4.2 Inner Produets and Orthogonal Matrices(158) 5.4.3 Four Basle Subspaees(163) Practice 5 Chapter 6 Eigenvalues 6.1 Eigenvalues and Eigenvecto 6.2 Diagonalizatio' 6.2.1 Similar Matriees and Diagonal Forms(172) 6.2.2 Applieatio ( 178 ) 6.3 Real Symmetric Matrices and Quadratic Forms 6.3.1 Canonical Forms for Real Symmetric Matrices 6.3.2 Quadratic Forms 6.3.3 Quadratic Expressio and Their Canonical Forms 6.4 Positive Definite Matrices and Classification of Quadratic Forms 6.4.1 Positive Definite Matrices 6.4.2 Optimization 6.4.3 Generalized Eigenvalue Problems Practice 6 Chapter 7 Linear Traformatio 7.1 Basic Concepts of Linear Traformatio 7.1.1 Linear Traformatio 7.1.2 Range and Kernel for a Linear Traformation 7.2 Linear Traformatio and Matrices 7.2.1 Coordinate Vecto 7.2.2 The Matrix Representatio for Linear Traformatio 7.2.3 Engenvalues and Eigenvecto of a Linear Traformation Practice 7 References
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