Syllabus
Matrices, Linear equations, and solvability:
Vector spaces
Basis and dimension
Linear transforms
Similarity of matrices
Rank-Nullity theorem and its applications:
Eigenvalues and eigenvectors
Cayley-Hamilton theorem and diagonalization
Inner-product spaces
Gram-Schmidt process
Optimization:
Unconstrained optimization: Gradient descent and Stochastic gradient descent methods.
Constrained optimization: Lagrange multiplier, Linear and dynamic programming, Bellman's principle of optimality.
Text Books
- Elizabeth Meckes and Mark W. Meckes, Linear Algebra, Cambridge University Press, 2018.
- Edwin K.P. Chong and Stanislaw H. Zak, Introduction to optimization, Wiley, 2013.
References
- Sheldon Axler, Linear Algebra Done Right, Springer, 2015.
- Linear Algebra and Optimization for Machine Learning, Charu Aggarwal, Springer, 2020.
- Linear Algebra and its Applications, 4th Edition, Gilbert Strang, Cengage India Private Limited; 2005.