At the end of this course, the student will acquire the basics of vector spaces and linear transformations and will be able to apply them to solve problems in diverse areas.
Vector Spaces: Vector Spaces, Subspaces, Linear independence, Basis and dimension, Linear transformations, Kernel and image of a linear transformation, dimension theorem, Inner product, Gram-Schmidt orthogonalization process, Orthogonal complement, Orthogonal projections. Applications of Linear Transformations: Lines and planes, Quadratic forms, Conic sections, Quadratic surfaces, Least squares, Differential equations and other applications. Eigenvalues and Eigenvectors: Polynomials of matrices and linear operators, Eigenvalues and eigenvectors, Diagonalization, Characteristic polynomial, Cayley-Hamilton theorem, Minimum polynomial, Jordan Canonical Form, Rational canonical form.
A combination of lectures and tutorial discussions .
Based on tutorials, tests and end of course examination .