### Linear Algebra

##### Table of Contents

- System of Linear Equations
- Linear Transformation and Matrix
- Vector and Matrix
- Linear Transformation
- Onto
- One-to-one
- Composition and Matrix Multiplication
- Inverse
- Transpose
- Partitioned Matrix
- Appendix: Transformation

- Vector Space
- Vector Space
- Subspace
- Linear Transformation
- Range and Column Space
- Kernel and Null Space
- Span
- Linear Independence
- Basis
- Computation of Basis
- Rank and Nullity
- Change of Basis
- Dual
- Direct Sum
- Appendix: Field

- Determinant
- Geometry of Determinant
- Computation of Determinant
- Properties of Determinant
- Theory of Determinant
- Proof of Properties

- Eigenvalue and Eigenvector
- Eigenvalue and Eigenvector
- Complex Diagonalization
- Application
- Properties
- Eigenspace and Multiplicity
- Polynomials of Matrix
- Appendix: Polynomial

- Inner Product
- Inner Product Space
- Duality and Adjoint
- Orthogonality
- Orthogonal and orthonormal
- Properties of orthogonality
- Orthonormal basis and isometry

- Orthogonal Projection
- Orthogonal projection
- Gram-Schmidt process

- Orthogonal Complement
- Definition and properties
- Complementarity principle

- Complex Inner Product
- Definition and properties
- Complementarity principle