Overview

This course aims to introduce students to all the basic and advanced concepts in Linear Algebra with a strong focus on applications. Linear Algebra is one of the fundamental tools that has applications in diverse fields such as Machine Learning, Data Analytics, Signal Processing, Wireless Communication, Operations Research, Control and Finance. The various topics and applications that will be covered in different areas are as follows:

Wireless: MIMO/ OFDM systems, Beamforming, Channel Estimation
Machine Learning: Regression, Clustering, EM Algorithm, Perceptron, SVM/ Kernel SVM, Principal Component Analysis (PCA), Face recognition
Signal Processing: Signal Estimation, Regularization, Compressive Sensing, Image Compression, Robotics and Dynamical systems
Data Analytics: Recommender systems, Data completion, Data prediction, forecasting, Optimal Estimation, Financial models
Operations Resarch: Markov chains, inventory management, supply chain management
Miscellaneous Applications: Electrical circuits, Graph models and social networks, Traffic flow management

The course is suitable for all UG/PG students and practicing engineers/ scientists/ managers from the diverse fields mentioned above and interested in learning about the novel cutting edge applications of linear algebra in various fields such as Machine Learning, Data Analytics, Signal Processing, Wireless Communication.

INTENDED AUDIENCE : -Students in Electrical Engineering, Electronics and Communication Engineering, Mathematics, Economics, Computer Science
-Practicing engineers -Technical and Non-technical managers of Telecomm companies
-Students preparing for Competitive Exams with focus on Wireless Communication, Signal Processing, Machine Learning
- Students pursuing projects or research in Machine Learning, Data Analytics and Signal Processing/ Communication PREREQUISITES : NoneINDUSTRIES SUPPORT :Qualcomm, Intel, Samsung, Google and other technology companies

Syllabus

COURSE LAYOUT

Week 1:Introduction to vectors, properties and applicationsWeek 2:Introduction to matrices and Applications – Circuits, Graphs, Social Networks, Traffic flowWeek 3:Eigenvalue decomposition, properties and Applications – Principal component analysis (PCA), Eigenfaces for facial recognitionWeek 4:Singular value decomposition (SVD) and Applications – Beamforming in MIMO, Dimensionality reduction, Rate maximization in wireless, MUSIC algorithm
Week 5:Linear regression and Least Squares. Applications: System identification, linear regression, Support vector machines (SVM), kernel SVMsWeek 6:Optimal linear MMSE estimation. Applications – MMSE Receiver, Market prediction and forecasting, ARMA modelsWeek 7:Data analytics: Recommender systems, user rating prediction, NETFLIX problemWeek 8:Structure of FFT/ IFFT matrices, properties, System model for OFDM/ SC-FDMA, Signal processing in OFDM systems. Modeling of Dynamical systems – Examples: Robots, Chemical plants. Solution of autonomous linear dynamical systems (LDS), solution of with inputs and outputs
Week 9:Modeling of Dynamical systems – Examples: Robots, Chemical plants. Solution of autonomous linear dynamical systems (LDS), solution of with inputs and outputsWeek 10:Unsupervised learning: Centroid based clustering, probabilistic model based clustering and EM algorithmWeek 11:Linear perceptron. Training a perceptron – stochastic gradient. Compressive sensing, orthogonal matching pursuit for sparse signal estimationWeek 12:Discrete time Markov chains – Applications: supply chain management, forecasting, Operations research – resource and inventory management.