Advanced linear algebra
Semester : VI
Course Code : 18MAT653
CIE Marks : 40 SEE Marks : 60
Full Notes
ADVANCED LINEAR ALGEBRA
18mat653
SYLLABUS
Module-1
Linear Equations: Consistent and inconsistent systems and its solution sets; LU-decomposition.
Vector Spaces: Vector spaces; subspaces; Linearly independent and dependent vectors; Bases and dimension;
coordinate vectors; computations concerning subspaces-Illustrative examples.
Module-2
Linear Transformations: Linear transformations; algebra of transformations; representation of
transformations by matrices; linear functional; Non singular Linear transformations; inverse of a linear
transformation; Problems on Rank-Nullity theorem.
Module-3
Inner Product Spaces: Inner products; inner product spaces; orthogonal sets and orthogonal projections;
Gram-Schmidt orthogonalization process; QR- decomposition.
Module-4
Introduction to Spectral Theory: Eigen values and eigenvectors; Diagonalization; quadratic
Forms, constrained optimization; Singular value decomposition.
Module-5
Engineering Applications:
i) Graphs and Networks.
ii) Matrices in Engineering.
iii) Computer Graphics.