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Advanced linear algebra

Semester :  VI

Course Code : 18MAT653

CIE Marks : 40                       SEE Marks : 60

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.