Syllabus
Vector Space: Basis and Dimensions – Change of Basis, Orthogonality – Fundamental Vector Spaces Associated with a Matrix, Matrix Decompositions: LU, QR, Eigen Decomposition and SVD, Cayley Hamilton Theorem, Fourier Transform and Fourier Basis
Function Optimization – Constrained and Unconstrained Optimization – Linear Programming – Linear Regression – Ordinary Least Squares – Gradient Descent – Conjugate Gradient Descent – Lagrange Multipliers – KKT Multipliers – ADMM – SVM
Random Variables – Moments – Covariance and Correlation – Probability Distributions – Moment generating functions – Transforming a random variable and Jacobean- Central limit theorem. Bayes Theorem – Naïve Bayes Classification – Parameter Estimation: MLE – Statistical testing: Mean of two random variables and statistical testing for proportions.