Mathematics for Machine Learning: Linear Algebra
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| Content Rating | 9.2 |
Throughout the course, we will learn, how linear algebra is relevant to machine learning and data science? We look at operations we can do with vectors. How to use matrices as tools to solve linear algebra problems. How matrices can transform a description of a vector from one basis (set of axes) to another, will allow us to apply a reflection to an image and manipulate images. Then we will go through special ‘Eigen-things’ that are very useful in linear algebra and will let us examine Google’s famous PageRank algorithm for presenting web search results.
About this Course
In this course on Mathematics for Machine Learning, we take a look at what linear algebra is and how it associates with vectors and matrices. Then we check out what vectors and matrices are and how to deal with them, consisting of the knotty issue of eigenvalues and eigenvectors, and how to utilize these to resolve issues. Finally, we take a look at how to utilize these to do enjoyable things with datasets – like how to turn pictures of faces and how to draw out eigenvectors to take a look at how the Pagerank algorithm works.
Since we’re focusing on data-driven applications, we’ll be carrying out a few of these concepts in code, not simply on pencil and paper. Towards completion of the course, you’ll compose code blocks and encounter Jupyter note pads in Python, however, do not fret, these will be rather brief, concentrated on the principles, and will assist you through if you’ve not coded prior to.
At the completion of this course, you will have a user-friendly understanding of vectors and matrices that will assist you to bridge the space into linear algebra issues, and how to use these principles in machine learning.
Syllabus:
This 5 weeks course has been organized by Imperial College of London, a world top ten university.
In this very first module, we take a look at how linear algebra pertains to machine learning and information science. Then we’ll end up the module with a preliminary intro to vectors. Throughout, we’re concentrating on establishing your mathematical instinct, not of crunching through algebra or doing long pen-and-paper examples. For much of these operations, there are callable functions in Python that can do the building up – the point is to value what they do and how they work so that, when things fail or there are special cases, you can comprehend why and what to do.
In this module, we take a look at operations we can do with vectors – discovering the modulus (size), angle in between vectors (dot or inner item) and forecasts of one vector onto another. We can then take a look at how the entries explaining a vector will depend upon what vectors we utilize to specify the axes – the basis. That will then let us identify whether a proposed set of basis vectors are what’s called ‘linearly independent.’ This will finish our evaluation of vectors, enabling us to proceed to matrices in module 3 and after that begin to resolve linear algebra issues.
Now that we’ve taken a look at vectors, we can rely on matrices. First we take a look at how to utilize matrices as tools to resolve linear algebra issues, and as items that change vectors. Then we take a look at how to resolve systems of linear formulas utilizing matrices, which will then take us on to take a look at inverse matrices and factors, and to think of what the factor truly is, intuitively speaking. Finally, we’ll take a look at cases of unique matrices that suggest that the factor is no or where the matrix isn’t invertible – cases where algorithms that require to invert a matrix will stop working.
In Module 4 of the Mathematics for Machine Learning course, we continue our conversation of matrices; initially, we think of how to code up matrix multiplication and matrix operations utilizing the Einstein Summation Convention, which is a commonly utilized notation in advanced linear algebra courses. Then, we take a look at how matrices can change a description of a vector from one basis (set of axes) to another. This will enable us to, for example, find out how to use a reflection to an image and control images. We’ll likewise take a look at how to build a practical basis vector set in order to do such changes. Then, we’ll compose some code to do these changes and use this work computationally.
Eigenvectors are specific vectors that are unrotated by a change matrix, and eigenvalues are the quantity by which the eigenvectors are extended. These unique ‘eigen-things’ are extremely helpful in linear algebra and will let us take a look at Google’s popular PageRank algorithm for providing web search results page. Then we’ll use this in code, which will conclude the course.
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Description
About this Course
In this course on Mathematics for Machine Learning, we take a look at what linear algebra is and how it associates with vectors and matrices. Then we check out what vectors and matrices are and how to deal with them, consisting of the knotty issue of eigenvalues and eigenvectors, and how to utilize these to resolve issues. Finally, we take a look at how to utilize these to do enjoyable things with datasets – like how to turn pictures of faces and how to draw out eigenvectors to take a look at how the Pagerank algorithm works.
Since we’re focusing on data-driven applications, we’ll be carrying out a few of these concepts in code, not simply on pencil and paper. Towards completion of the course, you’ll compose code blocks and encounter Jupyter note pads in Python, however, do not fret, these will be rather brief, concentrated on the principles, and will assist you through if you’ve not coded prior to.
At the completion of this course, you will have a user-friendly understanding of vectors and matrices that will assist you to bridge the space into linear algebra issues, and how to use these principles in machine learning.
Syllabus:
This 5 weeks course has been organized by Imperial College of London, a world top ten university.
In this very first module, we take a look at how linear algebra pertains to machine learning and information science. Then we’ll end up the module with a preliminary intro to vectors. Throughout, we’re concentrating on establishing your mathematical instinct, not of crunching through algebra or doing long pen-and-paper examples. For much of these operations, there are callable functions in Python that can do the building up – the point is to value what they do and how they work so that, when things fail or there are special cases, you can comprehend why and what to do.
In this module, we take a look at operations we can do with vectors – discovering the modulus (size), angle in between vectors (dot or inner item) and forecasts of one vector onto another. We can then take a look at how the entries explaining a vector will depend upon what vectors we utilize to specify the axes – the basis. That will then let us identify whether a proposed set of basis vectors are what’s called ‘linearly independent.’ This will finish our evaluation of vectors, enabling us to proceed to matrices in module 3 and after that begin to resolve linear algebra issues.
Now that we’ve taken a look at vectors, we can rely on matrices. First we take a look at how to utilize matrices as tools to resolve linear algebra issues, and as items that change vectors. Then we take a look at how to resolve systems of linear formulas utilizing matrices, which will then take us on to take a look at inverse matrices and factors, and to think of what the factor truly is, intuitively speaking. Finally, we’ll take a look at cases of unique matrices that suggest that the factor is no or where the matrix isn’t invertible – cases where algorithms that require to invert a matrix will stop working.
In Module 4 of the Mathematics for Machine Learning course, we continue our conversation of matrices; initially, we think of how to code up matrix multiplication and matrix operations utilizing the Einstein Summation Convention, which is a commonly utilized notation in advanced linear algebra courses. Then, we take a look at how matrices can change a description of a vector from one basis (set of axes) to another. This will enable us to, for example, find out how to use a reflection to an image and control images. We’ll likewise take a look at how to build a practical basis vector set in order to do such changes. Then, we’ll compose some code to do these changes and use this work computationally.
Eigenvectors are specific vectors that are unrotated by a change matrix, and eigenvalues are the quantity by which the eigenvectors are extended. These unique ‘eigen-things’ are extremely helpful in linear algebra and will let us take a look at Google’s popular PageRank algorithm for providing web search results page. Then we’ll use this in code, which will conclude the course.
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Specification:
- Coursera
- Imperial College London
- Online Course
- Self-paced
- Beginner
- Less Than 24 Hours
- Free Trial (Paid Course & Certificate)
- English
- Basic Maths
- Eigenvalues And Eigenvectors Linear Algebra Essentials Machine learning Transformation Matrix
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