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Mathematics for Machine Learning: Linear Algebra · LearnSpace
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Mathematics for Machine Learning: Linear Algebra

Курс от Imperial College London
Начальный≈ 18.8 чФранцузский
О курсеНавыкиПрограммаПреподаватели

О курсе

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.

Навыки, которые вы освоите

Linear AlgebraData TransformationComputational ThinkingData ScienceMachine LearningData ManipulationDimensionality ReductionApplied MathematicsJupyter

Программа курса

5 модулей · 68 учебных материалов

01Introduction to Linear Algebra and to Mathematics for Machine Learning14 материалов

Welcome to this course

Introduction: Solving data science challenges with mathematicsВидеоAbout Imperial College & the teamЧтениеHow to be successful in this courseЧтениеGrading policyЧтение

Учитесь у экспертов

David Dye

Professor of Metallurgy

Samuel J. Cooper

Associate Professor

A. Freddie Page

Strategic Teaching Fellow

Mathematics for Machine Learning: Linear Algebra
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Обучение на Coursera

≈ 18.8 ч

5 модулей

Язык: Французский

Субтитры: Арабский, Бенгальский, Узбекский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Вьетнамский, Нидерландский, Корейский, Немецкий, Пушту, Урду, Русский, Тайский, Индонезийский, Шведский, Турецкий, Английский, Азербайджанский, Испанский, Дари, Хинди, Японский, Казахский, Венгерский, Польский

Часть программы вашего университета
Additional readings & helpful referencesЧтение
Nice to meet you!Обсуждение
Complete our short pre-course surveyPLUGIN

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

Motivations for linear algebraВидеоGetting a handle on vectorsВидеоExploring parameter space ЗаданиеSolving some simultaneous equationsЗадание

Vectors

Operations with vectorsВидеоDoing some vector operationsЗадание

Summary

SummaryВидео
02Vectors are objects that move around space12 материалов

Introduction

Introduction to module 2 - VectorsВидео

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

Modulus & inner productВидеоCosine & dot productВидеоProjectionВидеоDot product of vectorsЗадание

Changing the reference frame

Changing basisВидеоChanging basisЗаданиеBasis, vector space, and linear independenceВидеоApplications of changing basisВидеоLinear dependency of a set of vectorsЗадание

Doing some real-world vectors examples

Vector operations assessmentЗаданиеSummaryВидео
03Matrices in Linear Algebra: Objects that operate on Vectors12 материалов

Introduction to matrices

Matrices, vectors, and solving simultaneous equation problemsВидео

Matrices in linear algebra: operating on vectors

How matrices transform spaceВидеоTypes of matrix transformationВидеоComposition or combination of matrix transformationsВидеоUsing matrices to make transformationsЗадание

Matrix Inverses

Solving the apples and bananas problem: Gaussian eliminationВидеоGoing from Gaussian elimination to finding the inverse matrixВидеоSolving linear equations using the inverse matrixЗадание

Special matrices and Coding up some matrix operations

Determinants and inversesВидеоIdentifying special matricesЛабораторнаяSummaryВидеоIdentifying special matricesПрограммирование
04Matrices make linear mappings12 материалов

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

Introduction: Einstein summation convention and the symmetry of the dot productВидеоNon-square matrix multiplicationЗаданиеExample: Using non-square matrices to do a projectionЗадание

Matrices transform into the new basis vector set

Matrices changing basisВидеоDoing a transformation in a changed basisВидео

Making Multiple Mappings, deciding if these are reversible

Orthogonal matricesВидео

Recognising mapping matrices and applying these to data

The Gram–Schmidt processВидеоGram-Schmidt processЛабораторнаяExample: Reflecting in a planeВидеоReflecting BearЛабораторнаяGram-Schmidt ProcessПрограммированиеReflecting BearПрограммирование
05Eigenvalues and Eigenvectors: Application to Data Problems18 материалов

What are eigen-things?

Welcome to module 5ВидеоWhat are eigenvalues and eigenvectors?ВидеоSelecting eigenvectors by inspectionЗадание

Getting into the detail of eigenproblems

Special eigen-casesВидеоCalculating eigenvectorsВидеоCharacteristic polynomials, eigenvalues and eigenvectorsЗадание

When changing to the eigenbasis is really useful

Changing to the eigenbasisВидеоEigenbasis exampleВидеоDiagonalisation and applicationsЗаданиеVisualising Matrices and EigenPLUGIN

Making the PageRank algorithm

Introduction to PageRankВидеоPageRankЛабораторнаяPage RankПрограммирование

Eigenvalues and Eigenvectors: Assessment

Eigenvalues and eigenvectorsЗаданиеSummaryВидеоWrap up of this linear algebra courseВидеоDid you like the course? Let us know!ЧтениеPost-Course SurveyPLUGIN