Course content

The course includes: General vector spaces (linear independence, basis), spaces with inner product, orthonormal basis, Gram-Schmidt, change of basis, orthogonal matrices, linear
transformations (kernel, image, dimension theorem, associated matrices), eigenvalues and eigenvectors for linear transformations and matrices, eigenspaces, complex vector spaces, complex inner products, unitary and Hermitian matrices, singular value decomposition and Cayley-Hamilton's theorem. Applications may include Markov chains, population growth (Leslie matrices), game theory, systems of differential equations, Fourier analysis, and fractals.

Learning outcome

1. Knowledge. The student is familiar with basic concepts concerning general vector spaces, matrices and linear transformations: Linear independence, basis, inner product space, orthonormal basis, Gram-Schmidt process, change of basis, orthogonal matrices, kernel, range, eigenvalues, eigenvectors, and diagonalization. The student is familiar with several applications of linear algebra.

2. Skills. The student masters various alogrithms and methods to make calculations involving vector spaces, matrices and linear transformations. The student is able to write simple mathematical proofs.

Learning methods and activities

Lectures and exercises. Final grade based on written final examination. Retake of examination may be given as an oral examination.

Compulsory assignments

• Exercises

Recommended previous knowledge

MA1201 Linear algebra and geometry.

Course materials

Will be announced at the start of the course.

Credit reductions