Lec 06- Matrix: Determinant, Inverse Computation, Adjoint, Cofactor Concepts

Preview 30:02

Lec 07- Applications of Matrices: Solution of System of Linear equations, MIMO Wireless Technology

Preview 37:51

Lec 08- Applications of Matrices: Electric Circuits, Traffic flows

Preview 22:50

Lec 09- Applications of Matrices: Graph Theory, Social Networks, Dominance Directed Graph, Influential Node

Preview 34:17

Lec 10- Null Space of Matrix: Definition, Rank-Nullity Theorem, Application in Electric Circuits

Preview 34:56

Lec 11- Gram-Schmidt Orthogonalization

Preview 24:46

Lec 12- Gaussian Random Variable: Definition, Mean, Variance, Multivariate Gaussian, Covariance Matrix

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Lec 13- Linear Transformation of Gaussian Random Vectors

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Lec 14- Machine Learning Application: Gaussian Classification

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Lec 15- Eigenvalue: Definition, Characteristic Equation, Eigenvalue Decomposition

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Lec 16- Special Matrices: Rotation and Unitary Matrices, Application: Alamouti Code

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Lec 17- Positive Semi-definite (PSD) Matrices: Definition, Properties, Eigenvalue Decomposition

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Lec 18- Positive Semidefinite Matrix: Example and Illustration of Eigenvalue Decomposition

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Lec 19- Machine Learning Application: Principle Component Analysis (PCA)

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Lec 20- Computer Vision Application: Face Recognition, Eigenfaces

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Lec 21- Least Squares (LS) Solution, Pseudo-Inverse Concept

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Lec 22- Least Squares (LS) via Principle of Orthogonality, Projection Matrix, Properties

Preview 32:41

Lec 23- Application: Pseudo-Inverse and MIMO Zero Forcing (ZF) Receiver

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Lec 24- Wireless Application: Multi-Antenna Channel Estimation

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Lec 25- Machine Learning Application: Linear Regression

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Lec 26- Computation Mathematics Application: Polynomial Fitting

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Lec 27- Least Norm Solution

Preview 38:39

Lec 28- Wireless Application: Multi-user Beamforming

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Lec 29- Singular Value Decomposition (SVD): Definition, Properties, Example

Preview 32:58

Lec 30- SVD Application in MIMO Wireless Technology: Spatial-Multiplexing and High Data Rates

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Lec 31- SVD for MIMO wireless optimization, water-filling algorithm, optimal power allocation

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Lec 32- SVD application for Machine Learning: Principal component analysis (PCA)

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Lec 33- Multiple signal classification (MUSIC) algorithm: system model

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Lec 34- MUSIC algorithm for Direction of Arrival (DoA) estimation

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Lec 35- Linear minimum mean square error (LMMSE) principle

Preview 30:09

Lec 36- LMMSE estimate and error covariance matrix

Preview 24:49

Lec 37- LMMSE estimation in linear systems

Preview 32:33

Lec 38- LMMSE application: Wireless channel estimation and example

Preview 34:45

Lec 39- Time-series prediction via auto-regressive (AR) model

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Lec 40- Recommender system: design and rating prediction

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Lec 41- Recommender system: Illustration via movie rating prediction example

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Lec 42- Fast Fourier transform (FFT) and Inverse fast Fourier transform (IFFT)

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Lec 43- IFFT/ FFT application in Orthogonal Frequency Division Multiplexing (OFDM) wireless technology

Preview 35:46

Lec 44- OFDM system: Circulant matrices and properties

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Lec 45- OFDM system model: Transmitter and receiver processing

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Lec 46- Single-carrier frequency division for multiple access (SC-FDMA) technology

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Lec 47- Linear dynamical systems: definition and solution via matrix exponential

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Lec 48- Linear dynamical systems: matrix exponential via SVD

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Lec 49- Machine Learning application: Support Vector Machines (SVM)

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Lec 50- Support Vector Machines (SVM): Problem formulation via maximum hyperplane separation

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Lec 51- Sparse regression: problem formulation and relation to Compressive Sensing (CS)

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Lec 52- Sparse regression: solution via the Orthogonal Matching Pursuit (OMP) algorithm

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Lec 53- OMP Example for Sparse Regression

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Lec 54- Machine Learning Application: Clustering

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Lec 55- K-Means Clustering algorithm

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Lec 56- Introduction to Stochastic Processes and Markov Chains

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Lec 57- Discrete Time Markov Chains and Transition Probability Matrix

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Lec 58- Discrete Time Markov Chain Examples

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Lec 59- m-STEP Transition Probabilities for Discrete Time Markov Chains

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Lec 60- Limiting Behavior of Discrete Time Markov Chains

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Lec 61- Least Squares Revisited: Rank Deficient Matrix

Preview 26:52

Lec 62- Least Squares using SVD

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Lec 63- Weighted Least Squares

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Lec 64- Weighted Least Squares Example

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Lec 65- Woodbury Matrix Identity - Matrix Inversion Lemma

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Lec 66- Woodbury Matrix Identity - Proof

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Lec 67- Conditional Gaussian Density - Mean

Preview 27:17

Lec 68- Conditional Gaussian Density - Covariance

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Lec 69- Scalar Linear Model for Gaussian Estimation

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Lec 70- MMSE Estimate and Covariance for the Scalar Linear Model

Preview 20:38

Live Session 15-03-2021

Preview 59:35