Curriculum | Linear Algebra (Code-09050602)

Linear Algebra (Code-09050602)

Curriculum

S.No.

Content of the topics

Learning Objectives

Teaching
Guidelines

Methodology

Time
(Hour))

1

  • Vector Spaces
  • Subspaces, sum and direct sum of subspaces
  • Linear span
  • Linearly dependent and independent subsets of vector space
  • Finitely generated vector space &Existence theorem for  basis of a finitely generated vector space
  • Finite dimensional vector spaces
  • Invariance of no. of elements of basis set, Dimensions
  • Quotient space and its dimension
 

 

 

Student s will know about the vector Spaces, its subspaces, basis and quotient spaces

 

 

Lecture should be effective so that student will be able to grasp the topics easily

 

Assignments/ Seminar/   Class Tests/ Presentation

12

2

  • Homomorphism and isomorphism of vector spaces
  • Linear transformations and linear  form of vector spaces
  • Vector spaces of all the linear transformations
  • Dual spaces, Bi-dual spaces
  • Annihilator of subspaces of finite dimensional vector spaces
  • Null space, Range space of a linear transformation, Rank & Nullity theorem
  • Algebra of linear transformations
  • Minimal polynomial of linear transformation
  • Singular & Non –Singular linear transformation
  • Matrix of a linear transformation
  • Change of basis
  • Eigen values and Eigen vector of linear transformations
 

 

 

 

Students will know about the homomorphism of vector spaces

 

 

 

Lecture should be effective so that student will be able to grasp the topics easily

Assignments/ Seminar/   Class Tests/ Presentation

14

3

  • Algebra of linear transformations
  • Minimal polynomial of linear transformation
  • Singular & Non –Singular linear transformation
  • Matrix of a linear transformation
  • Change of basis
  • Eigen values and Eigen vector of linear transformations
 

 

Students will know the algebra of linear transformation

 

Lecture should be effective so that student will be able to grasp the topics easily

Assignments/ Seminar/   Class Tests/ Presentation

8

4

  • Inner product spaces
  • Cauchy Schwarz inequality
  • Orthogonal vectors, orthogonal complements
  • Orthogonal sets and basis
  • Bessel’s inequality for finite dimensional vector spaces
  • Gram-Schmidt Orthogonalization process
  • Adjoint of a linear transformation and its properties
  • Unitary Linear Transformations
 

 

 

Students will know the inner Product Spaces

 

 

Lecture should be effective so that student will be able to grasp the topics easily

 

Assignments/ Seminar/   Class Tests/ Presentation

10

Admission Open- 2018