Lecture 1 - Vectors and Matrices - Linear Independence and Rank
Lecture 2 - Eigenvectors and Eigenvalues of Matrices and their Properties
Lecture 3 - Positive Semidefinite (PSD) and Postive Definite (PD) Matrices and their Properties
Lecture 4 - Inner Product Space and it's Properties: Linearity, Symmetry and Positive Semi-definite
Lecture 5 - Inner Product Space and it's Properties: Cauchy Schwarz Inequality
Lecture 6 - Properties of Norm, Gaussian Elimination and Echleon form of matrix
Lecture 7 - Gram Schmidt Orthogonalization Procedure
Lecture 8 - Null Space and Trace of Matrices
Lecture 9 - Eigenvalue Decomposition of Hermitian Matrices and Properties
Lecture 10 - Matrix Inversion Lemma (Woodbury identity)
Lecture 11 - Introduction to Convex Sets and Properties
Lecture 12 - Affine Set Examples and Application
Lecture 13 - Norm Ball and its Practical Applications
Lecture 14 - Ellipsoid and its Practical Applications
Lecture 15 - Norm Cone,Polyhedron and its Applications
Lecture 16 - Applications: Cooperative Cellular Transmission
Lecture 17 - Positive Semi Definite Cone And Positive Semi Definite (PSD) Matrices
Lecture 18 - Introduction to Affine functions and examples
Lecture 19 - norm balls and Matrix properties:Trace,Determinant
Lecture 20 - Inverse of a Positive Definite Matrix
Lecture 21 - Example Problems: Property of Norms,Problems on Convex Sets
Lecture 22 - Problems on Convex Sets (Continued...)
Lecture 23 - Introduction to Convex and Concave Functions
Lecture 24 - Properties of Convex Functions with examples
Lecture 25 - Test for Convexity: Positive Semidefinite Hessian Matrix
Lecture 26 - Application: MIMO Receiver Design as a Least Squares Problem
Lecture 27 - Jensen's Inequality and Practical Application
Lecture 28 - Jensen's Inequality application
Lecture 29 - Properties of Convex Functions
Lecture 30 - Conjugate Function and Examples to prove Convexity of various Functions
Lecture 31 - Examples on Operations Preserving Convexity
Lecture 32 - Examples on Test for Convexity, Quasi-Convexity
Lecture 33 - Examples on Convex Functions
Lecture 34 - Practical Application: Beamforming in Multi-antenna Wireless Communication
Lecture 35 - Practical Application: Maximal Ratio Combiner for Wireless Systems
Lecture 36 - Practical Application: Multi-antenna Beamforming with Interfering User
Lecture 37 - Practical Application: Zero-Forcing (ZF) Beamforming with Interfering User
Lecture 38 - Practical Application: Robust Beamforming With Channel Uncertainity for Wireless Systems
Lecture 39 - Practical Application: Robust Beamformer Design for Wireless Systems
Lecture 40 - Practical Application: Detailed Solution for Robust Beamformer Computation in Wireless Systems Text
Lecture 41 - Linear modeling and Approximation Problems: Least Squares
Lecture 42 - Geometric Intuition for Least Squares
Lecture 43 - Practical Application: Multi antenna channel estimation
Lecture 44 - Practical Application:Image deblurring
Lecture 45 - Least Norm Signal Estimation
Lecture 46 - Regularization: Least Squares + Least Norm
Lecture 47 - Convex Optimization Problem representation: Canonical form, Epigraph form
Lecture 48 - Linear Program Practical Application: Base Station Co-operation
Lecture 49 - Stochastic Linear Program,Gaussian Uncertainty
Lecture 50 - Practical Application: Multiple Input Multiple Output (MIMO) Beamforming
Lecture 51 - Practical Application: Multiple Input Multiple Output (MIMO) Beamformer Design
Lecture 52 - Practical Application: Co-operative Communication, Overview and various Protocols used
Lecture 53 - Practical Application: Probability of Error Computation for Co-operative Communication
Lecture 54 - Practical Application:Optimal power allocation factor determination for Co-operative Communication
Lecture 55 - Practical Application: Compressive Sensing
Lecture 56 - Practical Application
Lecture 57 - Practical Application- Orthogonal Matching Pursuit (OMP) algorithm for Compressive Sensing
Lecture 58 - Example Problem: Orthogonal Matching Pursuit (OMP) algorithm
Lecture 59 - Practical Application : L1 norm minimization and regularization approach for Compressive Sensing Optimization problem
Lecture 60 - Practical Application of Machine Learning and Artificial Intelligence:Linear Classification, Overview and Motivation
Lecture 61 - Practical Application: Linear Classifier (Support Vector Machine) Design
Lecture 62 - Practical Application: Approximate Classifier Design
Lecture 63 - Concept of Duality
Lecture 64 - Relation between optimal value of Primal and Dual Problems, concepts of Duality gap and Strong Duality
Lecture 65 - Example problem on Strong Duality
Lecture 66 - Karush-Kuhn-Tucker (KKT) conditions
Lecture 67 - Application of KKT condition:Optimal MIMO power allocation (Waterfilling)
Lecture 68 - Optimal MIMO Power allocation (Waterfilling)-II
Lecture 69 - Example problem on Optimal MIMO Power allocation (Waterfilling)
Lecture 70 - Linear objective with box constraints, Linear Programming
Lecture 71 - Example Problems II
Lecture 72 - Examples on Quadratic Optimization
Lecture 73 - Examples on Duality: Dual Norm, Dual of Linear Program (LP)
Lecture 74 - Examples on Duality: Min-Max problem, Analytic Centering
Lecture 75 - Semi Definite Program (SDP) and its application:MIMO symbol vector decoding
Lecture 76 - Application:SDP for MIMO Maximum Likelihood (ML) Detection
Lecture 77 - Introduction to big Data: Online Recommender System (Netflix)
Lecture 78 - Matrix Completion Problem in Big Data: Netflix-I
Lecture 79 - Matrix Completion Problem in Big Data: Netflix-II