Chapter 01 Overview of Linear Algebra
1.1 Basic Mathematical Concepts
1.2 Scope of linear algebra
1.3 Applications of linear algebra
Practice problems
Programming practice

Chapter 02 Linear Equations
2.1 Systems of linear equations
2.2 Solving simultaneous linear equations
2.3 Applications of simultaneous linear equations
Practice problems
Programming practice


Chapter 03 Matrix
3.1 Matrix
3.2 Matrix Operations
3.3 Inverse matrix
3.4 Special matrices
Practice problems
Programming practice

Chapter 04 Inverse Matrix
4.1 Calculating the inverse matrix
4.2 Application of the inverse matrix
4.3 LU decomposition
4.4 Inverse matrix of block matrix
Practice problems
Programming practice

Chapter 05 Determinant
5.1 Determinant
5.2 Properties of determinants
5.3 Determinant of block matrix
5.4 Geometric meaning of determinants
5.5 Applications of determinants
Practice problems
Programming practice
Chapter 06 Vectors
6.1 Vectors
6.2 Vector space
6.3 Dot product of vectors
6.4 Cross product of vectors
6.5 Vectors and Geometry
6.6 Differentiation of vectors and matrices
Practice problems
Programming practice

Chapter 07 Linear Transformation
7.1 Linear transformations
7.2 Subspaces and coefficients of linear transformations
Practice problems
Programming practice

Chapter 08 Eigenvalues ​​and Eigenvectors
8.1 Eigenvalues ​​and Eigenvectors
8.2 Properties of eigenvalues ​​and eigenvectors
8.3 Applications of Eigenvalues ​​and Eigenvectors
Practice problems
Programming practice


Chapter 09 Orthogonality
9.1 Orthogonal basis
9.2 Orthogonal decomposition
9.3 Least-squares solutions and optimal approximations of matrix equations
9.4 Applications of Orthogonality
Practice problems
Programming practice

Chapter 10 Diagonalization and Symmetry
10.1 Similarity and Diagonalization
10.2 Symmetric matrices
10.3 Quadratic form
10.4 Applications of Symmetric Matrices
Practice problems
Programming practice

Chapter 11 Singular Value Decomposition
11.1 Singular value decomposition
11.2 Applications of Singular Value Decomposition
Practice problems
Programming practice

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