Linear Algebra in every day life.- Basic mathematical concepts.- Algebraic structures.- Matrices.- The echelon form and the rank of matrices.- Linear systems of equations.- Determinants of matrices.- The characteristic polynomial and eigenvalues of matrices.- Vector spaces.- Linear maps.- Linear forms and bilinear forms.- Euclidean and unitary vector spaces.- Adjoints of linear maps.- Eigenvalues of endomorphisms.- Polynomials and the Fundamental Theorem of Algebra.- Cyclic subspaces, duality and the Jordan canonical form.- Matrix functions and systems of differential equations.- Special classes of endomorphisms.- The singular value decomposition.- The Kronecker product and linear matrix equations.
