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
- Bases, Dimension, and Linear Transformations
- Linear Transformations, Matrices, and Rank
- Independence