Lec 07- Gram Schmidt Orthogonalization Procedure

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Lec 08- Null Space and Trace of Matrices

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Lec 09- Eigenvalue Decomposition of Hermitian Matrices and Properties

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Lec 10- Matrix Inversion Lemma (Woodbury identity)

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Lec 11- Introduction to Convex Sets and Properties

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Lec 12- Affine Set Examples and Application

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Lec 13- Norm Ball and its Practical Applications

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Lec 14- Ellipsoid and its Practical Applications

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Lec 15- Norm Cone,Polyhedron and its Applications

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Lec 16- Applications: Cooperative Cellular Transmission

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Lec 17- Positive Semi Definite Cone And Positive Semi Definite (PSD) Matrices

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Lec 18-Introduction to Affine functions and examples

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Lecture 19-norm balls and Matrix properties:Trace,Determinant

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Lecture 20-Inverse of a Positive Definite Matrix

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Lecture 21-Example Problems: Property of Norms,Problems on Convex Sets

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Lecture 22-Problems on Convex Sets(contd.)

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Lecture 23-Introduction to Convex and Concave Functions

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Lecture 24-Properties of Convex Functions with examples

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Lec 25-Test for Convexity: Positive Semidefinite Hessian Matrix

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Lec 26-Application: MIMO Receiver Design as a Least Squares Problem

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Lec 27-Jensen's Inequality and Practical Application

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Lec 28-Jensen's Inequality application

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Lec 29 - Properties of Convex Functions

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Lec 30 - Conjugate Function and Examples to prove Convexity of various Functions

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Lec 31- Example problems: Operations preserving Convexity(log-sum, average) and Quasi Convexity

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Lec 32-Example Problems: Verify Convexity, Quasi -Convexity and Quasi- Concavity of functions

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Lec 33-Example Problems:Perspective function, Product of Convex functions and Pointwise Maximum is Convex

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Lec 34- Practical Application: Beamforming in Multi-antenna Wireless Communication

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Lec 35 - Practical Application: Maximal Ratio Combiner for Wireless Systems

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Lec 36- Practical Application: Multi-antenna Beamforming with Interfering User

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Lec 37- Practical Application: Zero-Forcing (ZF) Beamforming with Interfering User

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Lec 38- Practical Application: Robust Beamforming With Channel Uncertainity for Wireless Systems

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Lec 39- Practical Application: Robust Beamformer Design for Wireless Systems

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Lec 40 - Practical Application: Detailed Solution for Robust Beamformer Computation in Wireless Systems Text

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Lec 41- Linear modeling and Approximation Problems: Least Squares

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Lec 42-Geometric Intuition for Least Squares

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Lec 43- Practical Application: Multi antenna channel estimation

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Lec 44- Practical Application:Image deblurring

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Lec 45- Least Norm Signal Estimation

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Lec 46- Regularization: Least Squares + Least Norm

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Lec 47- Convex Optimization Problem representation: Canonical form, Epigraph form

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Lec 48-Linear Program Practical Application: Base Station Co-operation

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Lec 49- Stochastic Linear Program,Gaussian Uncertainty

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Lec 50- Practical Application: Multiple Input Multiple Output (MIMO) Beamforming

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Lec 51- Practical Application: Multiple Input Multiple Output (MIMO) Beamformer Design

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Lec 52-Practical Application: Co-operative Communication, Overview and various Protocols used

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Lec 53- Practical Application: Probability of Error Computation for Co-operative Communication

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Lec 54- Practical Application:Optimal power allocation factor determination for Co-operative Communication

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Lec 55- Practical Application: Compressive Sensing

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Lec 56- Practical Application

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Lec 57- Practical Application- Orthogonal Matching Pursuit (OMP) algorithm for Compressive Sensing

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Lec 58- Example Problem: Orthogonal Matching Pursuit (OMP) algorithm

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Lec 59- Practical Application : L1 norm minimization and regularization approach for Compressive Sensing Optimization problem

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Lec 60- Practical Application of Machine Learning and Artificial Intelligence:Linear Classification, Overview and Motivation

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Lec 61- Practical Application: Linear Classifier (Support Vector Machine) Design

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Lec 62- Practical Application: Approximate Classifier Design

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Lec 63- Concept of Duality

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Lec 64-Relation between optimal value of Primal & Dual Problems, concepts of Duality gap and Strong Duality

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Lec 65-Example problem on Strong Duality

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Lec 66- Karush-Kuhn-Tucker(KKT) conditions

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Lec 67- Application of KKT condition:Optimal MIMO power allocation(Waterfilling)

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Lec 68- Optimal MIMO Power allocation(Waterfilling)-II

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Lec 69- Example problem on Optimal MIMO Power allocation(Waterfilling)

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Lec 70- Linear objective with box constraints, Linear Programming

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Lec 71- Example Problems II

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Lec 72- Examples on Quadratic Optimization

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Lec 73- Examples on Duality: Dual Norm, Dual of Linear Program(LP)

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Lec 74- Examples on Duality: Min-Max problem, Analytic Centering

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Lec 75- Semi Definite Program(SDP) and its application:MIMO symbol vector decoding

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Lec 76- Application:SDP for MIMO Maximum Likelihood(ML) Detection

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Lec 77- Introduction to big Data: Online Recommender System(Netflix)

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Lec 78- Matrix Completion Problem in Big Data: Netflix-I

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Lec 79- Matrix Completion Problem in Big Data: Netflix-II

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