Linear Algebra

1. Linear Equations and Matrices

1.1Introduction

1.2 Dot product and matrix multiplication

1.3 Matrix transformation

1.4 Linear systems

1.5 System of linear equations and solutions

1.6Homogeneous and non homogeneous system of linear equations

1.7LU factorization

2. Real Vector Spaces

2.1Introduction

2.2Real vector space

2.3Subspaces

2.4 Linear independence

2.5 Basis and dimension

2.6Homogeneous systems

2.7The rank of a matrix and applications

2.8Coordinates and change of basis

2.9Orthonormal bases in Rn

3. Eigenvalues Eigenvectors and Diagonalization

3.1Introduction

3.2EigenValues and eigenvectors

3.3Diagonalization

3.4Cayley hamilton theorem

4. Linear Transformations and Matrices

4.1 Introduction

4.2 The kernel and range of a linear transformation

4.3 The matrix of a linear transformation