Algebraic operations-Triangular, Diagonal, Scalar, Unit Matrices-Transpose, adjoint and inverse of a square matrix- Symmetric and Skew Symmetric matrix.
Hermition and skew Hermition matrices-Orthogonal and Unitary matrices: Rank of matrix-Eigen values and eigen vectors of linear operators-Solutions of Homogeneous linear equations, Solutions of non-homogeneous linear equations. Characteristic vectors of a square matrix
Elementary basic concepts, linear independence bases.
Inner product spaces
Algebra of linear transformations - Characteristics roots.
Reference Book:
1.A First Course in Linear Algebra Aloknath charabarti, Vijay Nicole Imprints Pvt.Ltd-2006. 2Linear Algebra, Second Edition, Kenneth Hoffman, Ray Kunze, PHI, Seventh Printing- July 2001
Text Book:
1. A Text Book of Modern Algebra R.Balakrishnan and M. Ramabadran, Vikas Publishing House Pvt. Ltd, New Delhi, 1979 Unit I: Chapter 1: Sections: 1.1-1.7. Unit II: Chapter 1: Sections: 1.8-1.9. Chapter 2: Sections: 2.9. Chapter 3: Sections 3.6-3.9. 2. Topics in Algebra by I.N. Herstein, Vani Educational Books A Division of vikas Publishing House Pvt Ltd, New Delhi, 1984. Unit III: Chapter 4: Sections: 4.1, 4.2. Unit IV: Chapter 4: Sections: 4.4. Unit V: Chapter 6: Sections: 6.1, 6.2.
