MALAVIYA NATIONAL INSTITUTE OF TECHNOLOGY, JAIPUR.
DEPARTMENT OF MATHEMATICS
SYLLABUS
MAT-622 Linear Algebra and theory of matrices
4 Credits( 3L+1T+0P)
Fields and linear equations.Vector Spaces, Sub Spaces, Linear combinations, spanning sets,
Basis and Dimensions, Linear Transformations. Rank and Nullity of linear Transformation.
Representation of transformations by matrices.
Duality and transpose of a linear
transformation. Linear Functionals. Dual Space.
Eigen values and Eigen Vectors. Characterstics Polynomials, minimal polynomials. Cayley
Hamilton’s
theorem,
Orthogonality,
Triangularization,
Diagonalization.
Gram – Schmidt Orthonormalization.
functions and adjoints.
Inner
Product
Orthogonal Projections.
Unitary and normal operators.
Spaces,
Linear
Spectral theorem for normal
operators.
Bilinear forms, symmetric and skew symmetric bilinear forms, Bilinear forms and vectors,
matrix of a bilinear form.
Books Recommended:
1. Linear Algebra, K. Hoffman and R. Kunze, PHI Learning, 2009.
2.Linear Algebra, S. Lang, Springer India, 2005.
3.Linear Algebra, M. Artin, Pearson Education.
4. Linear Algebra, Herstein, Wiley India Pvt. Ltd., 2006.