MA 106 : Linear Algebra
Course Code MA 106
Course Name Linear Algebra
Offered to UG
Pre-requisites NIl
Lecture 2
Tutorial 1
Practical 0
Credit 4
Reference 1. H. Anton, Elementary linear algebra with applications (8th Edition), John Wiley (1995).
2. G. Strang, Linear algebra and its applications (4th Edition), Thom- son (2006).
3. S. Kumaresan, Linear algebra - A Geometric approach, Prentice Hall of India (2000).
4. E. Kreyszig, Advanced engineering mathematics (8th Edition), John Wiley (1999).
Description Vectors in Rn, notion of linear independence and dependence, linear span of a set of vectors, vector subspaces of Rn, basis of a vector subspace. Systems of linear equations, matrices and Gauss elimination, row space, null space, and column space, rank of a matrix. Determinants and rank of a matrix in terms of determinants. Abstract vector spaces, linear transformations, matrix of a linear trans-formation, change of basis and similarity, rank-nullity theorem. Inner pro duct spaces, Gram-Schmidt pro cess, orthonormal bases, pro-jections and least squares approximation. Eigenvalues and eigenvectors, characteristic polynomials, eigenvalues of special matrices (orthogonal, unitary, hermitian, symmetric, skew-symmetric, normal). algebraic and geometric multiplicity, diagonaliza-tion by similarity transformations, spectral theorem for real symmetric matrices, application to quadratic forms.