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.
Este curso forma parte de Programa Especializado - Matemática aplicada al aprendizaje automático
Mathematics for Machine Learning: Linear Algebra
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Acerca de este Curso
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Resultados profesionales del estudiante
35%
comenzó una nueva carrera después de completar estos cursos
34%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
Habilidades que obtendrás
Eigenvalues And EigenvectorsBasis (Linear Algebra)Transformation MatrixLinear Algebra
Resultados profesionales del estudiante
35%
comenzó una nueva carrera después de completar estos cursos
34%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
Certificado para compartir
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Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Nivel principiante
Aprox. 23 horas para completar
Sugerido: 5 weeks of study, 2-5 hours/week
Inglés (English)
Subtítulos: Inglés (English)
Programa - Qué aprenderás en este curso
2 horas para completar
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.
2 horas para completar
5 videos (Total 28 minutos), 4 lecturas, 3 cuestionarios
5 videos
Motivations for linear algebra3m
Getting a handle on vectors9m
Operations with vectors11m
Summary1m
4 lecturas
About Imperial College & the team5m
How to be successful in this course5m
Grading policy5m
Additional readings & helpful references10m
3 ejercicios de práctica
Exploring parameter space20m
Solving some simultaneous equations15m
Doing some vector operations30m
2 horas para completar
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.
2 horas para completar
8 videos (Total 44 minutos)
8 videos
Modulus & inner product10m
Cosine & dot product5m
Projection6m
Changing basis11m
Basis, vector space, and linear independence4m
Applications of changing basis3m
Summary1m
4 ejercicios de práctica
Dot product of vectors15m
Changing basis15m
Linear dependency of a set of vectors15m
Vector operations assessment15m
3 horas para completar
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.
3 horas para completar
8 videos (Total 57 minutos)
8 videos
How matrices transform space5m
Types of matrix transformation8m
Composition or combination of matrix transformations8m
Solving the apples and bananas problem: Gaussian elimination8m
Going from Gaussian elimination to finding the inverse matrix8m
Determinants and inverses10m
Summary59s
2 ejercicios de práctica
Using matrices to make transformations30m
Solving linear equations using the inverse matrix30m
7 horas para completar
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.
7 horas para completar
6 videos (Total 53 minutos)
6 videos
Matrices changing basis11m
Doing a transformation in a changed basis4m
Orthogonal matrices6m
The Gram–Schmidt process6m
Example: Reflecting in a plane14m
2 ejercicios de práctica
Non-square matrix multiplication20m
Example: Using non-square matrices to do a projection30m
Revisiones
Principales revisiones sobre MATHEMATICS FOR MACHINE LEARNING: LINEAR ALGEBRA
por CSMar 31, 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.
por NSDec 22, 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.
por PLAug 25, 2018
Great way to learn about applied Linear Algebra. Should be fairly easy if you have any background with linear algebra, but looks at concepts through the scope of geometric application, which is fresh.
por ECSep 9, 2019
Excellent review of Linear Algebra even for those who have taken it at school. Handwriting of the first instructor wasn't always legible, but wasn't too bad. Second instructor's handwriting is better.
por VCJul 10, 2018
The content of the course is very relevant, and the instructors are really fun and helpful.My only suggestion is to upload revisions for each assessment, so we can understand what we are doing wrong.
por TSJun 28, 2019
Good course with nice lecturer.\n\nSome topics should be explain more in detail and have some further reading / exercise for practicing.\n\nFor overall, this course is worth the time and money spend.
por BWMar 4, 2019
Satisfactory. Most satisfactory. Actually, this course is possibly the best linear algebra MOOC class in terms of instructor teaching style and how they pick and convey the most insightful concepts.
por JVNov 10, 2018
Great content and direction. Only negative is the sometimes frustrating experience with the Jupyter Notebooks: debugging what has gone wrong is very difficult, due to a lack of good error messages.
por PGSep 13, 2019
Excellent course!! The Mathematics for Machine Leaning : Linear Algebra offered by the Imperial College of London it's a good step into building a strong foundation in the field of Linear Algebra.
por JVJun 29, 2018
This is the BEST course if anyone wants to learn linear algebra for machine learning. Lectures are clear and very understandable and quiz questions are great, too. Thank you for this great course.
por DVJun 24, 2019
This was a terrific course; the instructors' are passionate and knowledgeable about the course material, the assignments are engaging and relevant, and the length of the videos feels "just right".
por MSMay 7, 2018
Good, but sometimes it is neccessary to look for supporting materials. I took this course in combination with MIT course in LA and this offered another, more practice oriented, view on the topic.
por ASJul 11, 2019
It's a nice course but instructors should go in more details. It's mostly high school mathematics. I was expecting undergraduate level Linear Algebra. Otherwise it was a good learning experience.
por MKMar 18, 2020
Be careful as a beginner in coding. It might be frustrating from time to time. I have spent the majority of my timing on the coding . At the end worthwhile, but did not feel that way at that time
por RBJul 16, 2019
Excellent overview of Linear Algebra for those who had not formally taken up a course on the subject. I had taught myself linear algebra about 18 years back and this was a great refresher course
por VLAug 6, 2018
The concepts are explained well. However, might not be very useful for people who have some basic understanding of linear algebra. Taking this course is not as effective as reading the textbook.
por ADMar 2, 2020
Brilliantly explained, loved the use of different marker which helped to understand better. Only one suggestion, if the summary has the mathematical equations/python equivalent would be helpful.
por TDJun 6, 2018
The course is a great resource to brush up on the fundamentals of linear algebra and learn about the meaning behind the math.It prepares people for any further courses which use linear algebra.
por PBMar 7, 2019
It's been excellent so far as the instructor has mixed the basics of linear algebra and real world examples to highlight the application in machine learning. Looking forward to further videos.
por ADAug 6, 2018
I liked it!\n\nGood leturers who are really inteested in the subject. I've bben listening to lectures with much pleasure.\n\nInteresting assignments and quizes!\n\nHighly recommend the course.
ofrecido por
Imperial College London
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.
Acerca de Programa especializado Matemática aplicada al aprendizaje automático
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 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.
Preguntas Frecuentes
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