Chapter 1 Matrices 1.1 Basic Concepts of Matrix 1.1.1 Definition of Matrix 1.1.2 Special Matrices 1.1.3 Application Examples 1.2 Operations of Matrices 1.2.1 Linear operations of matrices 1.2.2 Multiplication of Matrices 1.2.3 Transpose of a Matrix 1.2.4 Application Examples 1.3 Matrix Inverses 1.3.1 Invertible Matrices 1.3.2 Orthogonal Matrices 1.4 Blocks of Matrices 1.4.1 Block Operations 1.4.2 Block diagonal matrices 1.5 Elementary Operations and Gauss-Jordan Elimination 1.5.1 Elementary Operations 1.5.2 Gauss-Jordan Elimination 1.6 Elementary Matrices and a Method for Finding A-1 1.6.1 Elementary Matrices 1.6.2 A Method for Finding A-1 MATLAB EXERCISES
Chapter 2 Determinants 2.1 Introduction to Determinants 2.1.1 Definitions of Determinants 2.1.2 On the Row(Column) Expansion 2.2 Properties and Evaluation of Determinants 2.2.1 Properties 2.2.2 Evaluation 2.3 Applications of Determinants 2.3.1 Adjugate Matrices and Inverse Formula 2.3.2 Cramer' s rule 2.3.3 Application Examples MATLAB EXERCISES
Chapter 3 Vector Spaces and Linear Systems 3.1 Linear Dependence and Independence 3.2 Vector Spaces 3.2.1 Definition and Examples 3.2.2 Subspaces 3.2.3 The span of a set of vectors 3.3 Basis and Dimension 3.4 Rank 3.5 Structure for Linear Systems Solution Set 3.5.1 Homogeneous Systems 3.5.2 Non-Homogeneous Systems MATLAB EXERCISES
Chapter 4 Eigenvalues and Eigenvectors 4.1 The Concepts of Eigenvalues and Eigenvectors 4.2 Diagonalization 4.3 Quadratic Forms and Positive Definite Matrices MATLAB EXERCISES
Chapter 5 Linear Transformations 5.1 Definition and Examples 5.2 Matrix Representations of Linear Transformations MATLAB EXERCISES
Chapter 6 MATLAB 6.1 Input and Output in MATLAB 6.2 Matrix Operations in MATLAB 6.2.1 Addition and Multiplication of Matrices 6.2.2 Backslash or Matrix Left Division 6.2.3 Exponentiation 6.3 Elementary Row Operations in MATLAB 6.4 Matrix Inverses in MATLAB 6.5 Vectors in MATLAB 6.6 Linear Combinations in MATLAB 6.6.1 The linear combination problem 6.6.2 The span problem 6.6.3 The linear independencedependence problem 6.7 Linear Transformations in MATLAB 6.8 MATLAB Functions 6.8.1 Programming Features I 6.8.2 M-files 6.9 Relational and Logical Operators 6.10 Columnwise Array Operators 6.11 Graphics Bibliography
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