Linear Algebra 2025

MSc Data Science, Semester 1

Course information

  • Programme: MSc Data Science, Semester 1
  • Course code: 115
  • Instructor: Srikanth B. Pai

Syllabus

  • Systems of linear equations, row reduction, and matrix operations
  • Vector spaces, subspaces, linear independence, spanning sets, bases, and dimension
  • Linear transformations, matrix representations, change of basis, rank, and nullity
  • Determinants, invertibility, and the rank–nullity theorem
  • Inner products, orthogonality, projections, and Gram–Schmidt orthonormalisation
  • Eigenvalues, eigenvectors, diagonalisation, invariant subspaces, and minimal polynomials
  • Cayley–Hamilton theorem, Schur decomposition, and simultaneous diagonalisation
  • Applications to data science, including matrix factorisations and geometric interpretations

Course materials

Assignments

Examinations