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Mathematics for Machine Learning: Linear Algebra
  • Level Foundation
  • المدة 19 ساعات hours
  • الطبع بواسطة Imperial College London
  • Offered by

عن

In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Finally we look at how to use these to do fun things with datasets - like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works. Since we're aiming at data-driven applications, we'll be implementing some of these ideas in code, not just on pencil and paper. Towards the end of the course, you'll write code blocks and encounter Jupyter notebooks in Python, but don't worry, these will be quite short, focussed on the concepts, and will guide you through if you've not coded before. At the end of this course you will have an intuitive understanding of vectors and matrices that will help you bridge the gap into linear algebra problems, and how to apply these concepts to machine learning.

الوحدات

Welcome to this course

    • 1 Videos
    • 4 Readings
    • 1 Discussion
    • 1 Plugin
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1 Discussions

  • Nice to meet you!

1 Videos

  • Introduction: Solving data science challenges with mathematics

4 Readings

  • About Imperial College & the team
  • How to be successful in this course
  • Grading policy
  • Additional readings & helpful references

The relationship between machine learning, linear algebra, and vectors and matrices

    • 2 Videos
    • 2 Assignment
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2 Assignment

  • Exploring parameter space
  • Solving some simultaneous equations

2 Videos

  • Motivations for linear algebra
  • Getting a handle on vectors

Vectors

    • 1 Videos
    • 1 Assignment
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1 Assignment

  • Doing some vector operations

1 Videos

  • Operations with vectors

Summary

    • 1 Videos
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1 Videos

  • Summary

Introduction

    • 1 Videos
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1 Videos

  • Introduction to module 2 - Vectors

Finding the size of a vector, its angle, and projection

    • 3 Videos
    • 1 Assignment
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1 Assignment

  • Dot product of vectors

3 Videos

  • Modulus & inner product
  • Cosine & dot product
  • Projection

Changing the reference frame

    • 3 Videos
    • 2 Assignment
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2 Assignment

  • Changing basis
  • Linear dependency of a set of vectors

3 Videos

  • Changing basis
  • Basis, vector space, and linear independence
  • Applications of changing basis

Doing some real-world vectors examples

    • 1 Videos
    • 1 Assignment
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1 Assignment

  • Vector operations assessment

1 Videos

  • Summary

Introduction to matrices

    • 1 Videos
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1 Videos

  • Matrices, vectors, and solving simultaneous equation problems

Matrices in linear algebra: operating on vectors

    • 3 Videos
    • 1 Assignment
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1 Assignment

  • Using matrices to make transformations

3 Videos

  • How matrices transform space
  • Types of matrix transformation
  • Composition or combination of matrix transformations

Matrix Inverses

    • 2 Videos
    • 1 Assignment
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1 Assignment

  • Solving linear equations using the inverse matrix

2 Videos

  • Solving the apples and bananas problem: Gaussian elimination
  • Going from Gaussian elimination to finding the inverse matrix

Special matrices and Coding up some matrix operations

    • 2 Videos
    • 1 Lab
    • 1 Programming
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1 Programming

  • Identifying special matrices

1 Labs

  • Identifying special matrices

2 Videos

  • Determinants and inverses
  • Summary

Matrices as objects that map one vector onto another; all the types of matrices

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Non-square matrix multiplication
  • Example: Using non-square matrices to do a projection

1 Videos

  • Introduction: Einstein summation convention and the symmetry of the dot product

Matrices transform into the new basis vector set

    • 2 Videos
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2 Videos

  • Matrices changing basis
  • Doing a transformation in a changed basis

Making Multiple Mappings, deciding if these are reversible

    • 1 Videos
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1 Videos

  • Orthogonal matrices

Recognising mapping matrices and applying these to data

    • 2 Videos
    • 2 Lab
    • 2 Programming
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2 Programming

  • Gram-Schmidt Process
  • Reflecting Bear

2 Labs

  • Gram-Schmidt process
  • Reflecting Bear

2 Videos

  • The Gram–Schmidt process
  • Example: Reflecting in a plane

What are eigen-things?

    • 2 Videos
    • 1 Assignment
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1 Assignment

  • Selecting eigenvectors by inspection

2 Videos

  • Welcome to module 5
  • What are eigenvalues and eigenvectors?

Getting into the detail of eigenproblems

    • 2 Videos
    • 1 Assignment
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1 Assignment

  • Characteristic polynomials, eigenvalues and eigenvectors

2 Videos

  • Special eigen-cases
  • Calculating eigenvectors

When changing to the eigenbasis is really useful

    • 2 Videos
    • 1 Plugin
    • 1 Assignment
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1 Assignment

  • Diagonalisation and applications

2 Videos

  • Changing to the eigenbasis
  • Eigenbasis example

Making the PageRank algorithm

    • 1 Videos
    • 1 Lab
    • 1 Programming
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1 Programming

  • Page Rank

1 Labs

  • PageRank

1 Videos

  • Introduction to PageRank

Eigenvalues and Eigenvectors: Assessment

    • 2 Videos
    • 1 Readings
    • 1 Plugin
    • 1 Assignment
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1 Assignment

  • Eigenvalues and eigenvectors

2 Videos

  • Summary
  • Wrap up of this linear algebra course

1 Readings

  • Did you like the course? Let us know!

Auto Summary

Explore the essentials of Linear Algebra in the context of Data Science and AI with "Mathematics for Machine Learning: Linear Algebra" on Coursera. This foundational course, led by expert instructors, delves into vectors, matrices, eigenvalues, and eigenvectors, blending theory with practical coding exercises in Python. Ideal for beginners, the course spans approximately 19 hours and offers a hands-on approach to applying linear algebra concepts in machine learning. Available with a Starter subscription, it's perfect for aspiring data scientists and AI enthusiasts.

David Dye
Instructors

David Dye

Samuel J. Cooper
Instructors

Samuel J. Cooper

A. Freddie Page
Instructors

A. Freddie Page