Free online courseLinear Algebra for Machine Learning
Duration of the online course: 6 hours and 57 minutes
New course
Explore linear algebra's vital role in machine learning with this comprehensive free online course. Perfect for AI enthusiasts. Enroll now to start learning!
In this free course, learn about
- Welcome and Course Overview
- Linear Equations and Geometric Intuition
- Core Tensor Concepts and Data Structures
- Matrices and Higher-Rank Tensors
- Tensor Operations and Reductions
- Solving Linear Systems and Visualizing Solutions
- Matrix Norms, Multiplication, and Special Matrices
- Matrix Inverses and Structured Matrices
- Matrix Operations in Machine Learning
- Eigenvalues, Determinants, and Eigendecomposition
- Singular Value Decomposition and the Pseudoinverse
- Trace, PCA, and Further Linear Algebra Tools
Course Description
Dive into the world of linear algebra with this comprehensive free online course tailored for machine learning enthusiasts. This course serves as an essential foundation for anyone looking to explore the intricacies of artificial intelligence. It offers a robust introduction to the fundamentals of linear algebra and its pivotal role in machine learning.
Begin your journey with an overview of machine learning foundations, and get acquainted with the concept of linear algebra. Gain insights through plotting systems of linear equations and engage in practical exercises to reinforce your learning. Expand your understanding by exploring the realm of tensors, scalars, vectors, and vector transposition.
Develop proficiency in norms and unit vectors, and explore the significance of basis, orthogonal, and orthonormal vectors. Master matrix tensors and get comfortable with generic tensor notation. Enjoy hands-on exercises on algebra data structures, and delve into essential tensor operations including the Hadamard product and tensor reduction. The course brings clarity to solving linear systems through substitution and elimination, with bonus insights offered through video content.
Progress further into understanding matrix properties, including the Frobenius norm, matrix multiplication, and the intricacies of symmetric and identity matrices. The course provides detailed exercises on matrix multiplication and challenges your understanding through matrix inversion, diagonal matrices, and orthogonal matrices.
Advance to more complex topics with the second segment focused on matrix operations, including applying matrices, affine transformations, and the exploration of eigenvectors and eigenvalues. Delve into matrix determinants and their applications, and gain expertise in eigendecomposition. Practical applications of eigenvectors and eigenvalues in machine learning are thoroughly covered.
Conclude your learning journey by exploring singular value decomposition and its applications in data compression. Further your understanding with the Moore-Penrose pseudoinverse and its role in regression analysis. Explore advanced topics such as the trace operator and principal component analysis, ensuring a well-rounded grasp of linear algebra for machine learning.
Course content
- Video class: Machine Learning Foundations: Welcome to the Journey 02m
- Exercise: Which pair forms the linear algebra component of the ML foundations series?
- Video class: What Linear Algebra Is — Topic 1 of Machine Learning Foundations 24m
- Exercise: Which statement about solutions to a system of linear equations is correct?
- Video class: Plotting a System of Linear Equations — Machine Learning Foundations Bonus Video 09m
- Exercise: Intersection of two linear motions
- Video class: Linear Algebra Exercise — Topic 2 of Machine Learning Foundations 02m
- Exercise: A system models cumulative energy as two linear functions: Design A starts on April 1 generating 1 kJ/day; Design B starts on May 1 generating 4 kJ/day. On which day do their total energies become equal?
- Video class: Tensors — Topic 3 of Machine Learning Foundations 02m
- Exercise: What best describes a tensor in machine learning and linear algebra?
- Video class: Scalars — Topic 4 of Machine Learning Foundations 13m
- Exercise: Which statement best describes a scalar tensor in linear algebra and ML libraries?
- Video class: Vectors and Vector Transposition — Topic 5 of Machine Learning Foundations 12m
- Exercise: What is the shape after transposing a 1D NumPy vector of length 3?
- Video class: Norms and Unit Vectors — Topic 6 of Machine Learning Foundations 15m
- Exercise: Which norm measures Euclidean distance from the origin
- Video class: Basis, Orthogonal, and Orthonormal Vectors — Topic 7 of Machine Learning Foundations 04m
- Exercise: Properties of Orthonormal Basis Vectors
- Video class: Matrix Tensors — Topic 8 of Machine Learning Foundations 08m
- Exercise: Which statement about matrix notation and indexing is correct?
- Video class: Generic Tensor Notation — Topic 9 of Machine Learning Foundations 06m
- Exercise: Which shape matches a batch of 32 RGB images at 28x28 pixels in the [batch, height, width, channels] format?
- Video class: Exercises on Algebra Data Structures — Topic 10 of Machine Learning Foundations 00m
- Exercise: If matrix Y has 3 rows and 5 columns, what are its dimensions in algebraic notation?
- Video class: Tensor Operations — Segment 2 of Subject 1, Intro to Linear Algebra, ML Foundations 01m
- Exercise: Which set of activities best describes Segment 2 in Linear Algebra for Machine Learning?
- Video class: Tensor Transposition — Topic 11 of Machine Learning Foundations 03m
- Exercise: Under matrix transposition, where does the element at position (i, j) move?
- Video class: Basic Tensor Arithmetic (The Hadamard Product) — Topic 12 of Machine Learning Foundations 06m
- Exercise: Element wise vs matrix multiplication in tensor libraries
- Video class: Tensor Reduction — Topic 13 of Machine Learning Foundations 03m
- Exercise: What is the result of applying a sum reduction with axis=0 to an m×n matrix?
- Video class: The Dot Product — Topic 14 of Machine Learning Foundations 05m
- Exercise: Compute the dot product of two vectors
- Video class: Exercises on Tensor Operations — Topic 15 of Machine Learning Foundations 00m
- Exercise: Choose the operation that multiplies two same-shaped matrices element-wise
- Video class: Solving Linear Systems with Substitution — Topic 16 of Machine Learning Foundations 04m
- Exercise: Use substitution to solve the system y = 3x and -5x + 2y = 2. What is x?
- Video class: Solving Linear Systems with Elimination — Topic 17 of Machine Learning Foundations 05m
- Exercise: Which method is typically best when no variable in a linear system has a coefficient of 1?
- Video class: Visualizing Linear Systems — Machine Learning Foundations Bonus Video 10m
- Exercise: Solve the linear system y = 3x and y = 1 + 5x/2. What is the intersection point
- Video class: Matrix Properties — Final Segment of Subject 1, Intro to Linear Algebra, ML Foundations 02m
- Exercise: Which concept quantifies the size of a matrix?
- Video class: The Frobenius Norm — Topic 18 of Machine Learning Foundations 05m
- Exercise: Which statement best defines the Frobenius norm of a matrix?
- Video class: Matrix Multiplication — Topic 19 of Machine Learning Foundations 25m
- Exercise: If A is an m x n matrix and B is an n x p matrix, what is the shape of the product AB?
- Video class: Symmetric and Identity Matrices — Topic 20 of Machine Learning Foundations 04m
- Exercise: Effect of the identity matrix on a vector
- Video class: Matrix Multiplication Exercises — Topic 21 of Machine Learning Foundations 00m
- Exercise: Effect of the 3x3 Identity Matrix on a 3x1 Vector
- Video class: Matrix Inversion — Topic 22 of Machine Learning Foundations 17m
- Exercise: Solving for w in y = X w using matrix inversion
- Video class: Diagonal Matrices — Topic 23 of Machine Learning Foundations 03m
- Exercise: What operation is equivalent to multiplying a diagonal matrix diag x by a vector y
- Video class: Orthogonal Matrices — Topic 24 of Machine Learning Foundations 05m
- Exercise: Which property makes inverting an orthogonal matrix computationally cheap
- Video class: Orthogonal Matrix Exercises — Topic 25 of Machine Learning Foundations 02m
- Exercise: Proving that I3 is an orthogonal matrix
- Video class: Linear Algebra II: Matrix Operations — Subject 2 of Machine Learning Foundations 17m
- Exercise: Best method to solve overdetermined linear systems in ML
- Video class: Applying Matrices — Topic 26 of Machine Learning Foundations 07m
- Exercise: Applying a matrix to a concatenated matrix of column vectors
- Video class: Affine Transformations — Topic 27 of Machine Learning Foundations 18m
- Exercise: Which geometric property is preserved by affine transformations applied via matrices?
- Video class: Eigenvectors and Eigenvalues — Topic 28 of Machine Learning Foundations 26m
- Exercise: Interpreting eigenvalues under flipping and scaling
- Video class: Matrix Determinants — Topic 29 of Machine Learning Foundations 08m
- Exercise: Compute the determinant of X where X equals [[4, 2], [-5, -3]]
- Video class: Determinants of Larger Matrices — Topic 30 of Machine Learning Foundations 08m
- Exercise: Recursion rounds needed for a 6x6 determinant
- Video class: Determinant Exercises — Topic 31 of Machine Learning Foundations 01m
- Exercise: Determinant and Invertibility
- Video class: Determinants and Eigenvalues — Topic 32 of Machine Learning Foundations 16m
- Exercise: Which statement best describes the relationship between determinant, eigenvalues, and volume scaling for a square matrix X?
- Video class: Eigendecomposition — Topic 33 of Machine Learning Foundations 12m
- Exercise: Eigendecomposition of real symmetric matrices
- Video class: Eigenvector and Eigenvalue Applications — Topic 34 of Machine Learning Foundations 13m
- Exercise: Implication of a zero eigenvalue
- Video class: Matrix Operations for Machine Learning — Final Segment of Subject 2, Linear Algebra II 03m
- Exercise: Which operation decomposes rectangular matrices and is critical in machine learning because data matrices are often non-square?
- Video class: Singular Value Decomposition — Topic 35 of Machine Learning Foundations 10m
- Exercise: For a real matrix A with 3 rows and 2 columns, which SVD factor dimensions are correct in A = U D V^T?
- Video class: Data Compression with SVD — Topic 36 of Machine Learning Foundations 11m
- Exercise: Why does truncating an SVD to the first k components enable strong image compression?
- Video class: The Moore-Penrose Pseudoinverse — Topic 37 of Machine Learning Foundations 12m
- Exercise: Moore-Penrose pseudoinverse via SVD
- Video class: Regression with the Pseudoinverse — Topic 38 of Machine Learning Foundations 18m
- Exercise: In an overdetermined linear model y ≈ Xw, what does computing w = X^+ y achieve?
- Video class: The Trace Operator — Topic 39 of Machine Learning Foundations 04m
- Exercise: How can the Frobenius norm of matrix A be computed using the trace operator?
- Video class: Principal Component Analysis (PCA) — Topic 40 of Machine Learning Foundations 08m
- Exercise: In PCA, what does the first principal component represent
- Video class: Linear Algebra Resources — Topic 41 of Machine Learning Foundations 06m
- Exercise: Which operation provides a pseudo-inverse for non-square matrices, enabling least-squares solutions to systems common in machine learning?
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