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I Semester

Title-Algebra (Code-09010101)

S.N Topic Domain Hours as per UGC
1 MATRICES AND ITS APPLICATION

1.    Symmetric ,Skew- Symmetric matrices

2.    Hermitian ,Skew- Hermitian matrices

3.    Elementary operations on matrices

4.    Rank of matrices ,inverse of matrices

5.    L.D and L.I. of rows and columns

6.    Eigen values, eigenvectors and Char. Equation of a matrix

7.    Minimal polynomial of a matrix

8.    Cayley Hamilton Theorem and find inverse of a matrix.

Must Know 15
2 SOLUTION OF EQUATIONS WTH THE HELP OF MATRICES

1.    Homogeneous and non Homogeneous

2.    Application of matrices to a system of linear equations,

3.    Theorems on consistency of a system of linear equation

4.    Unitary and orthogonal matrices,

5.    Bilinear and Quadratic forms of matrices

Must know 15
3 POLYNOMIAL EUATIONS

1.    Relation between the roots and coefficients of general polynomial equation in one variable,

2.    Solutions of polynomial equation having conditions on roots,

3.    Common roots and multiple

4.    Roots. Transformation of equations.

Must know

 

Nice to know

12

Book Recommended:

  1. S. Hall and S.R. Knight: Higher Algebra. H.M. Publications 1994.
  2. Shanti Narayan: A text Book of Matrices.
  3. Chandrika Prasad: Text Book on Algebra and Theory of Equations. Pothishala Private Ltd. Allahabad.
  4. Titu Andreescu and Dorin Andrica, Complex Number from A to Z Birkhauser. 2006
  5. Madhumangal Pal:Abstrat Algebra.PHI I earning Private Limited Delhi. 2013
  6. David C.Lay. Linear Algebra and us Applications 3rd Ed.. Pearson Education Asia.
  7. Indian Reprint. 2007.
  8. H.hardy Pure Mathematics. Universal Book Stall, New Delhi. 1989.
  9. I.S. Luther and I.B.S.Passi. Algebra vol – 1. 11. Narosa Publishing House New Delhi
Admissions Open 2019-20