NOC:Applied Linear Algebra for Signal Processing, Data Analytics and Machine Learning

Lecture 1 - Vector Properties: Addition, Linear Combination, Inner Product, Orthogonality, Norm

Lecture 2 - Vectors: Unit Norm Vector, Cauchy-Schwarz inequality, Radar Application

Lecture 3 - Inner Product Application: Beamforming in Wireless Communication Systems

Lecture 4 - Matrices, Definition, Addition and Multiplication of Matrices

Lecture 5 - Matrix: Column Space, Linear Independence, Rank of Matrix, Gaussian Elimination

Lecture 6 - Matrix: Determinant, Inverse Computation, Adjoint, Cofactor Concepts

Lecture 7 - Applications of Matrices: Solution of System of Linear equations, MIMO Wireless Technology

Lecture 8 - Applications of Matrices: Electric Circuits, Traffic flows

Lecture 9 - Applications of Matrices: Graph Theory, Social Networks, Dominance Directed Graph, Influential Node

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

Lecture 11 - Gram-Schmidt Orthogonalization

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

Lecture 13 - Linear Transformation of Gaussian Random Vectors

Lecture 14 - Machine Learning Application: Gaussian Classification

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

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

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

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

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

Lecture 20 - Computer Vision Application: Face Recognition, Eigenfaces

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

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

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

Lecture 24 - Wireless Application: Multi-Antenna Channel Estimation

Lecture 25 - Machine Learning Application: Linear Regression

Lecture 26 - Computation Mathematics Application: Polynomial Fitting

Lecture 27 - Least Norm Solution

Lecture 28 - Wireless Application: Multi-user Beamforming

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

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

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

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

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

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

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

Lecture 36 - LMMSE estimate and error covariance matrix

Lecture 37 - LMMSE estimation in linear systems

Lecture 38 - LMMSE application: Wireless channel estimation and example

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

Lecture 40 - Recommender system: design and rating prediction

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

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

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

Lecture 44 - OFDM system: Circulant matrices and properties

Lecture 45 - OFDM system model: Transmitter and receiver processing

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

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

Lecture 48 - Linear dynamical systems: matrix exponential via SVD

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

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

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

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

Lecture 53 - OMP Example for Sparse Regression

Lecture 54 - Machine Learning Application: Clustering

Lecture 55 - K-Means Clustering algorithm

Lecture 56 - Introduction to Stochastic Processes and Markov Chains

Lecture 57 - Discrete Time Markov Chains and Transition Probability Matrix

Lecture 58 - Discrete Time Markov Chain Examples

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

Lecture 60 - Limiting Behavior of Discrete Time Markov Chains

Lecture 61 - Least Squares Revisited: Rank Deficient Matrix

Lecture 62 - Least Squares using SVD

Lecture 63 - Weighted Least Squares

Lecture 64 - Weighted Least Squares Example

Lecture 65 - Woodbury Matrix Identity - Matrix Inversion Lemma

Lecture 66 - Woodbury Matrix Identity - Proof

Lecture 67 - Conditional Gaussian Density - Mean

Lecture 68 - Conditional Gaussian Density - Covariance

Lecture 69 - Scalar Linear Model for Gaussian Estimation

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