Vectors and Matrices - Addition and Multiplication – Bases - Linear independence and dependence of vectors – Orthogonal matrices - Rank of matrix - Finding Eigen values and eigen vectors of a matrix - Problems based on Rank – Nullity theorem.

Metrics - Lp Distances and their Relatives - Lp Distances - Mahalanobis Distance - Cosine and Angular Distance - KL Divergence - Distances for Sets and Strings - Jaccard Distance - Modeling Text with Distances - Bag-of-Words Vectors - k-Grams

Unconstrained Multivariate Optimization - Gradient Descent Learning Rule - Multivariate optimization with equality constraint – Multi variate optimization with in equality constraint

Cross validation – Multiple linear Regression modelling building and selection – Classification – Performance measures

Data Matrices - Projections - SSE Goal - Singular Value Decomposition - Best Rank-k Approximation Principal Component Analysis - Computation of PCA Components - Reduction of Two dimension data set to one dimension – Drawing Graph for PCA