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Title-Linear Algebra (Code-09010602)

S.No. Unit Contents Domain Hours as per UGC
1 One 1.      Vector Spaces

2.      Subspaces, sum and direct sum of subspaces

3.      Linear span

4.      Linearly dependent and independent subsets of vector space

5.      Finitely generated vector space &Existence theorem for  basis of a finitely generated vector space

6.      Finite dimensional vector spaces

7.      Invariance of no. of elements of basis set, Dimensions

8.      Quotient space and its dimension

Must Know 15
2 Two 1.      Homomorphism and isomorphism of vector spaces

2.      Linear transformations and linear form of vector spaces

3.      Vector spaces of all the linear transformations

4.      Dual spaces, Bidual spaces

5.      Annihilator of subspaces of finite dimensional vector spaces

6.      Null space, Range space of a linear transformation, Rank & Nullity theorem

7.      Algebra of linear transformations

8.      Minimal polynomial of linear transformation

9.      Singular & Non –Singular linear transformation

10.  Matrix of a linear transformation

11.  Change of basis

12.  Eigen values and Eigen vector of linear transformations

Must know 15
3 Three 1.      Inner product spaces

2.      Cauchy Schwarz inequality

3.      Orthogonal vectors, orthogonal complements

4.      Orthogonal sets and basis

5.      Bessel’s inequality for finite dimensional vector spaces

6.      Gram-Schmidt Orthogonalization process

Must know



Nice to know


Books Recommended:

  1. N. Herstein: topics in Algebra, Wiley Eastern Ltd., New Delhi, 1975
  2. Vivek Sahai and Vikas Bist: Algebra, Narosa Publishing House

I.S. Luther and I.B.S. Passi: Algebra, Vol-II, Narosa Publishing House.