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