Matrix Algebra

This course is aimed to review the basic concepts of linear algebra:

1. Systems of linear equations: solution by Gaussian elimination, PA=LU factorization, Gauss-Jordan method.
2. Vector spaces and subspaces, the four fundamental subspaces, and the fundamental theorem of linear algebra.
3. Determinant and eigenvalues, symmetric matrices, spectral theorem, quadratic forms.
4. Cayley-Hamilton theorem, functions of matrices, and application of linear algebra to dynamical linear systems.
5. Iterative methods for systems of linear equations.
6. Ordinary lest squares problem, normal equations, A=QR factorization, condition number, Tikhonov regularization.
7. Singular-value decomposition, Moonre-Penrose pseudoinverse.
8. An economic application of linear algebra: the Leontief input-outpul model.