Syllabus for Linear Algebra for Data Science

Learning outcomes

On completion of the course the student shall be able to:

• be able to give an account of and use basic vector space concepts such as linear space, linear dependence, basis, dimension, linear transformation,
• be able to give an account of and use basic concepts in the theory of finite dimensional Euclidean spaces,
• be familiar with the concepts of eigenvalue, eigenspace and eigenvector and know how to compute these objects,
• know the spectral theorem for symmetric operators,
• be able to compute the singular value decomposition of a matrix,
• account for how the concepts in the previous paragraph are theoretically connected,
• be able to use the theory, methods and techniques of the course to solve mathematical problems.

Content

Linear spaces: subspaces, linear span, linear dependence, basis, dimension, change of bases. Matrices: rank, column space and row space, rank factorization. Linear transformations: their matrix and its dependence on the bases, composition and inverse, range and nullspace, the dimension theorem. Euclidean spaces: inner product, the Cauchy-Schwarz inequality, orthogonality, ON-basis, orthogonalisation, orthogonal projection, isometry. Spectral theory: eigenvalues, eigenvectors, eigenspaces, characteristic polynomial, diagonalisability, the spectral theorem, singular value decomposition.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

This course cannot be included in the same degree as 1MA024 or 1MA323.