Applied Linear Algebra for Signal Processing, Data Analytics and Machine Learning | EveryEng

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

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914 min

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Why enroll

Participants join this course because it helps them clearly understand how Linear Algebra is used in real-world applications, not just as theory. The course explains concepts in a simple way and shows how they are applied in areas like machine learning, data analytics, signal processing, wireless communication, and finance. It is useful for students who want stronger fundamentals and for working professionals who want to upgrade their skills for modern technologies. By the end of the course, learners gain practical knowledge that helps them solve real problems, perform better in studies or jobs, and stay relevant in today’s technology-driven world.

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Is this course for you?

You should take this if

You work in Automotive
You're a Electrical Engineering professional
You have 3+ years of hands-on experience in this field
You want to build skills in Engineering & Design, Project Management

You should skip if

You're new to this field with no prior experience
You need a different specialisation outside Electrical Engineering
You need live interaction with an instructor

Course details

This course helps learners understand both the basics and advanced ideas of Linear Algebra, with a strong focus on how it is used in real life. Linear Algebra is a powerful math tool that plays a key role in many modern technologies and industries.

In this course, you will see how Linear Algebra is applied in different fields, such as:

Wireless Communication: Understanding MIMO and OFDM systems, beamforming, and how signals are estimated over communication channels.
Machine Learning: Learning how algorithms like regression, clustering, PCA, SVM, and face recognition work behind the scenes.
Signal Processing: Applying math to signal estimation, image compression, robotics, and dynamic systems.
Data Analytics: Building recommender systems, predicting and forecasting data, and understanding financial models.
Operations Research: Solving real-world problems using Markov chains, inventory control, and supply chain management.
Other Applications: Analyzing electrical circuits, social networks and graphs, and managing traffic flow efficiently.

This course is suitable for undergraduate and postgraduate students, as well as working professionals, engineers, scientists, and managers. It is ideal for anyone who wants to learn how Linear Algebra is used in modern fields like Machine Learning, Data Analytics, Signal Processing, and Wireless Communication in a clear and practical way.

Source: IIT-Kanpur Nptel [Youtube Channel]

Course suitable for

Key topics covered

Introduction to Linear Algebra and its importance
Basics of matrices and how they are used
Different types of matrices explained simply
Matrix addition and subtraction
Matrix multiplication made easy
Special matrices like zero and identity
Transpose of a matrix
Determinant and why it matters
Inverse of a matrix and its use
Solving linear equations using matrices
Row operations and matrix simplification
Gaussian elimination method
Rank of a matrix explained
Basics of vectors and vector operations
Introduction to eigenvalues and eigenvectors

Course content

The course is readily available, allowing learners to start and complete it at their own pace.

31 lectures15 hr 14 min

Applied Linear Algebra for Signal Processing, Data Analytics and Machine Learning
5 min
Applied Linear Algebra | Vector Properties
35 min
Vectores: Unit nom vector,Cauchy-Schwarz inequality, Radar application
31 min
Inner Product Application: Beamforming in Wireless Communication Systems
20 min
Matrices: Definition, Addition and Multiplication of Matrices
22 min
Matrix: Column Space, Linear Independence, Rank, Gaussian Elimination
29 min
Matrix: Determinant, Inverse Computation, Adjoint, Cofactor Concepts
30 min
Applications of Matrices: Solution of Linear Systems, MIMO Wireless Technology
37 min
Applications of Matrices: Electric Circuits, Traffic Flows
22 min
Applications of Matrices: Graph Theory, Social Networks, Dominance Directed Graph, Influential Node
34 min
Null Space of Matrix: Definition, Rank-Nullity Theorem, Application in Electric Circuits
34 min
Gram-Schmidt Orthogonalization
24 min
Gaussian Random Variable: Definition, Mean, Variance, Multivariate Gaussian, Covariance Matrix
16 min
Linear Transformation of Gaussian Random Vectors
19 min
Machine Learning Application: Gaussian Classification
34 min
Eigenvalue: Definition, Characteristic Equation, Eigenvalue Decomposition
33 min
Special Matrices: Rotation and Unitary Matrices; Application — Alamouti Code
39 min
Positive Semi-definite (PSD) Matrices: Definition, Properties, Eigenvalue Decomposition
35 min
Positive Semidefinite Matrix: Examples & Illustrations of Eigenvalue Decomposition
40 min
Machine Learning Application: Principal Component Analysis (PCA)
42 min
Computer Vision Application: Face Recognition, Eigenfaces
20 min
Least Squares (LS) Solution, Pseudo-Inverse Concept
38 min
Least Squares via Principle of Orthogonality, Projection Matrix, Properties
32 min
Application: Pseudo-Inverse and MIMO Zero Forcing (ZF) Receiver
34 min
Wireless Application: Multi-Antenna Channel Estimation
34 min
Machine Learning Application: Linear Regression
27 min
Computational Mathematics Application: Polynomial Fitting
14 min
Least Norm Solution
38 min
Wireless Application: Multi-user Beamforming
34 min
Singular Value Decomposition (SVD): Definition, Properties, Example
32 min
SVD Application in MIMO Wireless Technology: Spatial-Multiplexing & High Data Rates
30 min

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Questions and Answers

Q: You're debugging a Kalman-filtered sensor fusion block and searching "singular values exploding in covariance update automotive kalman filter". The innovation covariance goes non-positive-definite after a few seconds. Logs show the measurement matrix H is full rank on paper. What's the root cause?

A: Restoring numerical stability keeps P symmetric positive-definite across updates. Option B explains filter sluggishness but not loss of definiteness. Option C would show up immediately as dimension errors or gain mismatch. Option D doesn't create negative eigenvalues by itself.

Q: During bench validation you're googling "FFT magnitude mismatch datasheet vs measurement ADC windowing". The ADC datasheet claims 96 dB SNR with a Hann window, but your measured FFT tops out at ~90 dB. What's the first verification step?

A: Aligning definitions reconciles measurement with spec before touching hardware. Option B masks errors but doesn't fix scaling. Option C trades leakage for bias and breaks the comparison. Option D skips basic verification and burns schedule.

Q: Reviewing an ML pipeline doc while searching "PCA whitening matrix dimensions confusion", you see a block labeled "Whitening: W = Λ^{-1/2} U^T". The covariance is defined as Σ = (1/N)XX^T with X ∈ R^{m×N}. What's inconsistent?

A: Identifying the missing centering step prevents biased components. Option B flips the intent of whitening. Option C affects bias slightly but not orthogonality. Option D confuses dual formulations used when N<m.

Q: A lane-detection CNN shows training loss decreasing but validation accuracy flatlines. You're searching "rank deficient feature matrix gradient descent stagnation". Batch logs show many identical singular values in the feature covariance. Root cause?

A: Removing linear dependence restores informative gradient directions. Option B affects speed, not rank. Option C contradicts the observed loss trend. Option D is layer-specific and doesn't explain covariance structure.