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