To teach students the basic concepts of linear algebra such as vector spaces, linear independence, base, dimension, inner product spaces, linear transformation, eigenvalue, eigenvector and diagonalization.

Vector spaces, subspaces, linear independence, linear combinations. Stretching, base and dimension. Linear transformations, nucleus and image of a linear transformation. Isomorphisms, eigenvalues and eigenvectors. Characteristic polynomials. Diagonalization, inner product spaces, orthogonality of vectors, orthonormal vector sets.