Linear Algebra for Machine Learning: Vectors, Matrices, Eigenvalues and SVD
A code-driven linear algebra course that moves from tensors, vectors and matrix operations through linear systems, determinants, eigendecomposition, SVD and the pseudoinverse. Each topic is demonstrated in Python with NumPy, TensorFlow and PyTorch, and ties back to machine learning uses such as regression, data compression and PCA. It suits learners who want working intuition for the maths behind ML, rather than a proof-based treatment.
Lessons by Jon Krohn on YouTubeCurated by YodaHut. These lessons are hosted on YouTube and produced by their original creators, who are not affiliated with YodaHut. You still earn YodaCoins, keep your streak and track progress here.
What You'll Learn
- Create and manipulate scalars, vectors, matrices and higher-order tensors in NumPy, TensorFlow and PyTorch
- Compute norms, unit vectors, dot products, Hadamard products, transposes and tensor reductions, and apply matrix multiplication
- Solve systems of linear equations by substitution and elimination, and visualize them graphically
- Work with special matrices (identity, symmetric, diagonal, orthogonal) and find matrix inverses
- Calculate determinants for 2x2 and larger matrices, and explain how they relate to eigenvalues and eigenvectors
- Perform affine transformations, eigendecomposition and singular value decomposition, and use SVD for data compression
- Fit a regression line with the Moore-Penrose pseudoinverse and describe how PCA builds on these tools
Prerequisites
- Comfort with high-school algebra
- Basic Python familiarity helps for the code demos
- No prior linear algebra needed
Course Curriculum
- 1Welcome to the Machine Learning Foundations Series2:38
- 2What Linear Algebra Is24:04
- 3Plotting a System of Linear Equations9:19
- 4Linear Algebra Exercise: Solar Panels2:05
- 5Tensors2:34
- 6Scalars13:05
- 7Vectors and Vector Transposition12:19
- 8Norms and Unit Vectors15:10
- 9Basis, Orthogonal, and Orthonormal Vectors4:30
- 10Matrix Tensors8:24
- 11Generic Tensor Notation6:44
- 12Exercises on Algebra Data Structures0:42
- 13Tensor Operations: Segment Introduction1:20
- 14Tensor Transposition3:53
- 15Basic Tensor Arithmetic and the Hadamard Product6:13
- 16Tensor Reduction3:32
- 17The Dot Product5:14
- 18Exercises on Tensor Operations0:57
- 19Solving Linear Systems with Substitution4:04
- 20Solving Linear Systems with Elimination5:52
- 21Visualizing Linear Systems10:59
- 22Matrix Properties: Segment Introduction2:06
- 23The Frobenius Norm5:02
- 24Matrix Multiplication25:00
- 25Symmetric and Identity Matrices4:42
- 26Matrix Multiplication Exercises0:52
- 27Matrix Inversion17:07
- 28Diagonal Matrices3:26
- 29Orthogonal Matrices5:50
- 30Orthogonal Matrix Exercises2:11
- 31Linear Algebra II: Matrix Operations Overview17:53
- 32Applying Matrices7:32
- 33Affine Transformations18:53
- 34Eigenvectors and Eigenvalues26:47
- 35Matrix Determinants8:05
- 36Determinants of Larger Matrices8:42
- 37Determinant Exercises1:28
- 38Determinants and Eigenvalues16:16
- 39Eigendecomposition12:49
- 40Eigenvector and Eigenvalue Applications13:02
- 41Matrix Operations for Machine Learning: Segment Introduction3:22
- 42Singular Value Decomposition10:50
- 43Data Compression with SVD11:33
- 44The Moore-Penrose Pseudoinverse12:23
- 45Regression with the Pseudoinverse18:57
- 46The Trace Operator4:37
- 47Principal Component Analysis (PCA)8:27
- 48Linear Algebra Resources6:11
About the Instructor
Jon Krohn
YouTube creator
The lessons in this course were produced by Jon Krohn and are published on YouTube. YodaHut selected and sequenced them into this course; we did not make them, and Jon Krohn is not affiliated with YodaHut.
Visit the channel on YouTubeMore in the Library: Academics
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Linear Algebra: From Linear Systems to Eigenvalues and Least Squares
Linear Algebra (MIT 18.06): Matrices, Vector Spaces, Eigenvalues and SVD
Single Variable Calculus (MIT 18.01): Limits, Derivatives, Integrals and Series
Introductory Statistics and Probability: From Data Collection to Regression
- 48 lessons
- 6h 58m of video
- Earns YodaCoins & streaks
- Timestamped notes
- Free — hosted on YouTube
No certificate is issued for Library courses.