Gaussian elimination, LU decomposition. Vector Spaces , Bases, Orthogonal bases Infinite dimensional vector spaces Fourier Series and Fourier Transform and its properties Convolution Vector spaces associated with Matrices Projection matrices and its properties Cayley Hamilton theorem Diagonalizability of matrices Eigenvalues and Eigenvectors of Symmetric matrices Eigenvalues and Eigen vectors of ATA, AAT Relationship between vector spaces associated with A, ATA, AAT. Formulation of ordinary differential equation with constant coefficients in various engineering domains, Converting higher order into first order equations Numerical solution with Rungekutta method. Taylor series expansion of multivariate functions, conditions for maxima , minima and saddle points, Concept of gradient and hessian matrices Multivariate regression and regularized regression , Newton methods for optimization, Signal processing with regularized regression. Random variables and distributions, Expectation, variance , moments cumulants, Sampling from univariate distribution- various methods, Concept of Jacobian and its use in finding pdf of functions of Random variables(RVs), boxmuller formula for sampling normal distribution, Concept of correlation and Covariance of two linearly related RVs, Multivariate Gaussian distribution, Bayes theorem, Introduction to Bayesian estimation process, Markov chain, Markov decision process.
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