Applied Linear Algebra
- Linear Equations in Linear Algebra (linear systems and their solutions, matrices, the matrix equation, linear independence, linear transformations)
- Matrix Algebra ( matrix operations, inverse of matrix, matrix factorization, determinants)
- Vector Spaces ( vector spaces and subspaces, null space, column space, bases, dimension of a vector space, rank, change of basis)
- Eigenvalues and Eigenvectors (eigenvalues and eigenvectors, characteristic equation, diagonalization, applications)
- Orthogonality and Least Squares (inner products, orthogonal sets, The Gram-Schmidt process, least squares problems, applications)
- Singular Value Decomposition, Principal Component Analysis
- Optimization (vector functions, first and second order derivative, introduction to different types of optimization problems, linear programming, the simplex algorithm)