Course Details
Subject {L-T-P / C} : MA4107 : Linear Algebra { 3-1-0 / 4}
Subject Nature : Theory
Coordinator : Prof. Suvendu Ranjan Pattanaik
Syllabus
Vector spaces, Bases and dimensions, Sums and direct sums, Quotient spaces. Linear transformations, Kernel, and image of a linear transformation, Rank-nullity theorem, Representation of linear transformations by matrices, Change of bases for linear transformations, Base-change Matrices, Orthonormal bases, Gram-Schmidt process. Invariant subspaces, Cayley-Hamilton theorem, Minimal polynomial, Adjoint operators (matrix), Normal, unitary, and self-adjoint operators (matrix), Schur's Lemma, Spectral theorem for normal operators (matrix) (Unitary diagonalization, and triangulation of a matrix), Direct-sum decomposition, Cyclic subspaces, and Annihilators, Rational and Jordan canonical forms, LU and Cholesky decomposition, Householder’s Reflection, QR and Polar Decomposition, Tridiagonal Matrix, Strum’s Sequence, Projection Matrix, Singular value decomposition, Generalized inverse of the matrix, Perron–Frobenius theorem, Quadratic form. Sylvester inertia theorem, Linear functional, Bilinear mapping and inner product spaces.
Course Objectives
- To introduce the application of linear algebra and matrices in the different branches of mathematics.
- Introduce theoretical aspects of linear algebra required for recent evolving branches like machine learning and data analysis.
- Also, it extensively introduces students to generalized inverse, QR decomposition and SVD.
- Also, introduces Perron–Frobenius theorem, Quadratic form. Sylvester inertia theorem, Linear functional, Bilinear mapping.
Course Outcomes
Students should be well-versed in applying linear algebra and matrices in the different branches of mathematics (like machine learning and data analysis ).
Essential Reading
- K. Hoffman and R. A. Kunze, Linear Algebra, Prentice Hall of India
- H. Dym, Linear algebra in Action (Graduate studies in Mathematics, American Mathematical Society
Supplementary Reading
- R A Horn, C R Johnson, Matrix Analysis, Cambridge
- J H Kwak, S Hong, Linear Algebra, Birkhauser