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初級レベル

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推奨:5 weeks of study, 2-5 hours/week...

英語

字幕:英語

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Eigenvalues And EigenvectorsBasis (Linear Algebra)Transformation MatrixLinear Algebra

100%オンライン

自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

初級レベル

約21時間で修了

推奨:5 weeks of study, 2-5 hours/week...

英語

字幕:英語

シラバス - 本コースの学習内容

1
2時間で修了

Introduction to Linear Algebra and to Mathematics for Machine Learning

In this first module we look at how linear algebra is relevant to machine learning and data science. Then we'll wind up the module with an initial introduction to vectors. Throughout, we're focussing on developing your mathematical intuition, not of crunching through algebra or doing long pen-and-paper examples. For many of these operations, there are callable functions in Python that can do the adding up - the point is to appreciate what they do and how they work so that, when things go wrong or there are special cases, you can understand why and what to do.

...
5件のビデオ (合計28分), 4 readings, 3 quizzes
5件のビデオ
Motivations for linear algebra3 分
Getting a handle on vectors9 分
Operations with vectors11 分
Summary1 分
4件の学習用教材
About Imperial College & the team5 分
How to be successful in this course5 分
Grading policy5 分
Additional readings & helpful references10 分
3の練習問題
Exploring parameter space20 分
Solving some simultaneous equations15 分
Doing some vector operations14 分
2
2時間で修了

Vectors are objects that move around space

In this module, we look at operations we can do with vectors - finding the modulus (size), angle between vectors (dot or inner product) and projections of one vector onto another. We can then examine how the entries describing a vector will depend on what vectors we use to define the axes - the basis. That will then let us determine whether a proposed set of basis vectors are what's called 'linearly independent.' This will complete our examination of vectors, allowing us to move on to matrices in module 3 and then start to solve linear algebra problems.

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8件のビデオ (合計44分), 4 quizzes
8件のビデオ
Modulus & inner product10 分
Cosine & dot product5 分
Projection6 分
Changing basis11 分
Basis, vector space, and linear independence4 分
Applications of changing basis3 分
Summary1 分
4の練習問題
Dot product of vectors15 分
Changing basis15 分
Linear dependency of a set of vectors15 分
Vector operations assessment15 分
3
3時間で修了

Matrices in Linear Algebra: Objects that operate on Vectors

Now that we've looked at vectors, we can turn to matrices. First we look at how to use matrices as tools to solve linear algebra problems, and as objects that transform vectors. Then we look at how to solve systems of linear equations using matrices, which will then take us on to look at inverse matrices and determinants, and to think about what the determinant really is, intuitively speaking. Finally, we'll look at cases of special matrices that mean that the determinant is zero or where the matrix isn't invertible - cases where algorithms that need to invert a matrix will fail.

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8件のビデオ (合計57分), 3 quizzes
8件のビデオ
How matrices transform space5 分
Types of matrix transformation8 分
Composition or combination of matrix transformations8 分
Solving the apples and bananas problem: Gaussian elimination8 分
Going from Gaussian elimination to finding the inverse matrix8 分
Determinants and inverses10 分
Summary59
2の練習問題
Using matrices to make transformations12 分
Solving linear equations using the inverse matrix16 分
4
6時間で修了

Matrices make linear mappings

In Module 4, we continue our discussion of matrices; first we think about how to code up matrix multiplication and matrix operations using the Einstein Summation Convention, which is a widely used notation in more advanced linear algebra courses. Then, we look at how matrices can transform a description of a vector from one basis (set of axes) to another. This will allow us to, for example, figure out how to apply a reflection to an image and manipulate images. We'll also look at how to construct a convenient basis vector set in order to do such transformations. Then, we'll write some code to do these transformations and apply this work computationally.

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6件のビデオ (合計53分), 4 quizzes
6件のビデオ
Matrices changing basis11 分
Doing a transformation in a changed basis4 分
Orthogonal matrices6 分
The Gram–Schmidt process6 分
Example: Reflecting in a plane14 分
2の練習問題
Non-square matrix multiplication20 分
Example: Using non-square matrices to do a projection12 分
4.7
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Mathematics for Machine Learning: Linear Algebra からの人気レビュー

by NSDec 23rd 2018

Professors teaches in so much friendly manner. This is beginner level course. Don't expect you will dive deep inside the Linear Algebra. But the foundation will become solid if you attend this course.

by CSApr 1st 2018

Amazing course, great instructors. The amount of working linear algebra knowledge you get from this single course is substantial. It has already helped solidify my learning in other ML and AI courses.

講師

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David Dye

Professor of Metallurgy
Department of Materials
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Samuel J. Cooper

Lecturer
Dyson School of Design Engineering
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A. Freddie Page

Strategic Teaching Fellow
Dyson School of Design Engineering

インペリアル・カレッジ・ロンドン(Imperial College London)について

Imperial College London is a world top ten university with an international reputation for excellence in science, engineering, medicine and business. located in the heart of London. Imperial is a multidisciplinary space for education, research, translation and commercialisation, harnessing science and innovation to tackle global challenges. Imperial students benefit from a world-leading, inclusive educational experience, rooted in the College’s world-leading research. Our online courses are designed to promote interactivity, learning and the development of core skills, through the use of cutting-edge digital technology....

Mathematics for Machine Learningの専門講座について

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science. In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them. The second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting. The third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require basic Python and numpy knowledge. At the end of this specialization you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning....
Mathematics for Machine Learning

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