Applied Linear Algebra
- Introduction to the course, preliminaries
- Linear equations, Echelon form, solution sets of linear systems
- Linear independence – linear transformations
- Matrix operations, inverse of a matrix, partitioned matrix
- Matrix factorization
- Determinants and its properties, Cramer’s Rule
- Vector spaces and sub-spaces
- Dimensions, matrix rank, change of basis
- Eigenvalues and eigenvectors, characteristic equation
- diagonalization, iterative estimates to eigenvalues
- Inner product, orthogonality, 2-norm, orthogonal sets, Gram-Schmidt algorithm
- Least-square problems, inner product spaces
- Symmetric matrices and their diagonalization, quadratic form
- Constrained optimization, singular value decomposition
- An application of linear algebra to computer engineering