Linear Algebra for Data Science
Linear Algebra for Data Science
Linear Algebra for Data Science [MAL7050] (2 Credits)
Monday, Wednesday , Friday (4:00- 4:55 PM)
Internal -40 %
Quizzes- 40% (Four quizzes with equal weightage)
External-60%
Mid semester Examination I - 15%
Mid semester Examination II -15%
End semester Examination - 30%
The Quizzes will be conducted on August 10, August 29, September 14, and September 30, 2022.
Matrix Algebra : Matrix operations and type of matrices, Rank of Matrix, Eigenvalues, Eigenvectors, and Diagonalizable matrices, Vector spaces R^{n}, linear independence, basis, linear mappings, affine spaces, Vector Norms, Matrix Norms, lengths and distances, angles and orthogonality, orthogonal basis, orthogonal complement, inner product, orthogonal projections, matrix derivatives
Matrix Decompositions : Spectral decomposition, Schur Decomposition, QR Factorization, Singular value decomposition (SVD), Polar Decomposition, Pseudo Inverse.
Introduction: Condition of a linear system, condition of the eigenvalue problem, sparse matrices, numerical linear algebra software
Linear solvers : Direct methods and iterative methods (Gaussian elimination method, LU factorization method, Cholesky factorization method, QR factorization method, Householder’s method, Gradient descent, conjugate gradients, generalized minimal residual method preconditioning)
Computing eigenvalues : Direct methods and iterative methods(power iteration, inverse iteration, shifting, deflation, QR iteration, SVD decomposition, Krylov subspace methods, the Arnoldi and Lanczos methods)
Meyer, C. D., (2000) Matrix Analysis and Applied Linear Algebra, SIAM.
Strang, G., (2019), Linear Algebra and learning from data, Wellesley-Cambridge Press
Elden, L. (2007) Matrix Methods in Data Mining and Pattern Recognition, SIAM.
Deisenroth, M. P., Faisal, A. A. and Ong, C. S. (2019), Mathematics for machine learning, Cambridge University Press.