Basic ideas and concepts: vector, matrix, linear systems of equations, Gauss elimination, matrix factorization, complexity, vector geometry with inner product, cross product, determinant and vector space, linear independent, basis, linear transformation, eigenvalue, eigenvector, the least squares method, orthogonality, inner-product space, Gram-Schmidt's method, complex numbers, the inductions axiom, the fundamental theorem of the algebra.
Computational aspects: Solution to linear equation systems, Gauss elimination, the LU-factorization, condition number, full and sparse matrices, complexity, the least squares method, calculation of eigenvalues, eigenvectors and graphical visualization of results.