Linear Algebra

Linear Algebra

Introduction to Matrices

• Introduction and Basic Operations
• Matrix Multiplication
• Algebraic Properties of Matrix Operations
• Invertible Matrices
• Special Matrices: Triangular, Symmetric, Diagonal
• Elementary Operations for Matrices
• Matrix Exponential

• Applications:

  • Application of Invertible Matrices: Coding

  • Complex numbers as Matrices

  • Markov Chains

Systems of Linear Equations

• System of Equations: An Introduction

• Systems of Linear Equations: Gaussian Elimination

• Systems of linear equations in Two variables.

• Systems of linear equations in Three variables.

• Application of Determinant to Systems: Cramer's Rule

• More Problems on Linear Systems and Matrices

Determinants

• Introduction to Determinants

• Determinants of Matrices of Higher Order

• Determinant and Inverse of Matrices

• Application of Determinant to Systems: Cramer's Rule

Eigenvalues and Eigenvectors

• Eigenvalues and Eigenvectors: An Introduction

• Computation of Eigenvalues

• Computation of Eigenvectors

• The Case of Complex Eigenvalues

• Diagonalization