### 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.