SYLLABUS- LINEAR ALGEBRA, Unit-1: Vector spaces and their elementary properties, Subspaces, Linear
dependence and independence, Basis and dimension, Direct sum,
Quotient space.
Unit-2: Linear transformations and their algebra, Range and null space,
Rank and nullity, Matrix representation of linear transformations,
Change of basis.
Unit-3: Linear functionals, Dual space, Bi-dual space, Natural
isomorphism, Annihilators, Bilinear and quadratic forms, Inner product
spaces, Cauchy-Schwarz's inequality, Bessel's inequality and
orthogonality.