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Linear Algebra (Code-09050602)
SYLLABUS

S.No.

Contents

Domain

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

Must know

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

Must know

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

Must know

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

Nice to know

10

Books Recommended:

  • I.N. Herstein: topics in Algebra, Wiley Eastern Ltd., New Delhi, 1975
  • Vivek Sahai and Vikas Bist: Algebra, Narosa Publishing House
  • I.S. Luther and I.B.S. Passi: Algebra, Vol-II, Narosa Publishing House.
  • P.B. Bhattacharya, S.K. Jain and S.R. Nagpal: Basic Abstract Algebra(2nd edition).
  • Gilbert Strang: Linear Algebra and its applications, Thomson 2007
  • S. Kumarsen: Linear Algebra-A Geometric Approach, Prentic Hall of India Pvt. Ltd.,1999.
  • Kenneth Hoffman, Ray Alden Kunze: Linear Algebra, 2nd Ed., Prentic Hall of India Pvt. Ltd., 1971.
Admissions Open 2019-20