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|MA 2150||Linear Algebra and Optimization||3||-||-||3||SMA|
Vector Spaces, subspaces, basis, dimension. Linear Transformation and their representation by Matrices.
Matrices: Review of Matrix Algebra; Rank of matrix; Eigen-values and Eigen-vectors; Diagonalisation; Systems of Linear Equations; Quadratic surfaces.
Inner Product Spaces, Orthonormal Sets, Gram Schmidt orthogonalisation process and its applications to the method of least squares and QR algorithm.
Introduction to Optimization problems. Nature of Solutions and Algorithms.
1. C.W. Curtis Linear Algebra: An Introductory Approach. Springer, 1984.
2. G. Strang Introduction to Linear Algebra. Wellesley, MA: Wellesley-Cambridge Press, 1993.
3. D.G. Luenberger, Linear and Nonlinear Programming , Addison – Wesley, 1984.
4. A.D. Belegundu and T.R. Chandrupatla Optimization Concepts and Applications in Engineering, Pearson Education Asia, 2002.