Linear algebra plays an important role in solving problems arising in a variety
of application domains including engineering, machine learning, data
science, and more. This course is a continuation of MAT203 (Applied Linear
Algebra) with focuses on computational linear algebra and its applications to
real-world problems. It provides analysis of the problems along with algorithms
and also uses python or Matlab as tool for implementing algorithms. It provides
an instruction for programming in python (or Matlab) in the context of scientific
computing.

Topics include basic linear algebra, stability and accuracy of numerical algorithms,
various matrix factorizations (QR, SVD, LU, etc.), principal component analysis,
iterative methods for linear systems, computation of eigenvalues and eigenvectors,
randomized linear algebra, and its applications to various fields such as
Google's PageRank algorithm, machine learning, data mining, computer vision.

Knowledge of undergraduate linear algebra and calculus. Python will
be used as the primary language and you will be expected to master it at the end
of the semester.

30% homework
35% midterm
35% final exam

Basics: Introduction, motivation, overview, review of programming language (python); conditioning, stability and accuracy of numerical algorithms

Review of linear algebra: multiplication, matrix-matrix multiplication, fundamental subspaces, orthogonal matrices

Eigendecompositions: computing eigenvalues and eigenvectors; power method and inverse iteration

Orthogonal vectors and matrices; QR decomposition and its computation

Singular value decomposition (SVD) and Principal component analysis (PCA):
reduction; low rank approximation; computing SVD

Solving linear equations and least squares; iterative methods; Arnoldi and Krylov iteration;

Randomized linear algebra: matrix-matrix multiplication and randomized Kaczmarz iteration

Applications: Google's PageRank; Low rank and compressed sensing; Classification of handwritten digits; Deep learning

No late homework will be accepted without an approved excuse.