MA2101 Linear Algebra via Matrices [Only for 2024 batch onwards]

Course Details

Matrix operations:
Basic operations, Transpose and adjoint, Elementary row operations, RREF, Determinant, Computing matrix inverse.
Systems of linear equations:
Linear independence, Rank, Solvability, Gauss-Jordan elimination and Gauss elimination.
Matrix as a linear map:
subspace and span, Basis & dimension, Linear transformation, Coordinate vectors, Coordinate matrices, Change of basis matrix, Equivalence and similarity.
Orthogonality:
Inner products, Gram-Schmidt process, QR-factorization, Orthogonal projection, Best approximation, Least squares solutions.
Eigenvalues and Eigenvectors:
The characteristic polynomial, spectrum, Special types of matrices.
Canonical forms:
Schur triangularization, Annihilating polynomials, Diagonalizability, Jordan form, Singular value decomposition.

Course References:

Text:
A. Singh, Introduction to Matrix Theory, Springer, 2021.
Reference:
G. Strang, Introduction to Linear Algebra, 6th Ed., Wellesley-Cambridge Press, 2023.