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LINEAR ALGEBRA [1]

Paper Code: 
MAT 221
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Unit I: 
I
15.00

Linear transformation of vector spaces, Dual spaces, Dual basis and their properties, Dual maps, Annihilator. 

Unit II: 
II
15.00

Matrices of a linear maps, Matrices of composition maps, Matrices of dual map, Eigen values, Eigen vectors, Rank and Nullity of linear maps and matrices, Invertible matrices, Similar matrices.

Unit III: 
III
15.00
Determinants of matrices and its computations, Characteristic polynomial and eigen values.Minimal polynomial, Cayley-Hamiltton theorem.
 
Unit IV: 
IV
15.00

Bilinear forms: Definition and examples. The matrix of a Bilinear form, Orthogonality, Classification of Bilinear forms.

Unit V: 
V
15.00

Real inner product space, Schwartzs inequality, Orthogonality, Bessel’s inequality, Adjoint, Self adjoint linear transformations and matrices, Othogonal linear transformation and matrices, Principal Axis Theorem.

Essential Readings: 
  1. Kenneth Hoffman & Ray Kunze, ‘Linear Algebra’, Prentice-Hall of India.
  2. K.B.Datta,’Matrix and Linear Algebra’, Prentice-Hall of India.
  3. A. Ramachandra Rao and Bhimasankaram, Linear Algebra, Second Edition, Hindustan Book Agency
References: 
  1. M. Artin, ‘Algebra’, Prentice-Hall of India.
  2. Ben Noble, James W. Daniel, ‘Applied Linear Algebra’, Prentice-Hall of India.
  3. I.N. Herstein, Topics in Algebra, Second Edition, Wiley Eastern Ltd.
 
Academic Year: 
2014-2015 [2]

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[1] https://maths.iisuniv.ac.in/courses/subjects/linear-algebra-5
[2] https://maths.iisuniv.ac.in/academic-year/2014-2015