21670 - Linear Algebra for Data Science
This course is designed to present and discuss those aspects of Linear Algebra that are most important in Data Analytics. The emphasis will be on developing intuition and understanding how to use linear algebra, rather than on "proofs".
The main topics will include:
- Basic matrix operations, linear transformations.
- Subspaces, ranges and null spaces, linear combinations and spans, linear independence, bases, dimension, rank and nullity theorem.
- Systems of linear equations, symmetric matrices, inverses, determinants, triangular matrices, trace, eigenvalues and eigenvectors.
- Positive definite matrices, covariance matrices, minimization problems involving vectors and matrices, minimization and convex functions.
- Orthogonal projections, Gram-Schmidt procedure, singular value decomposition.
- Tensor structures.