Hi, I did that article :)
Saludos
Introduction to Linear Algebra for Applied Machine Learning with Python
11–20 of 54 posts
Re: Introduction to Linear Algebra for Applied Machine Learning with Python
#12Earlier quoted context omitted.
One of the fun things about linear algebra is that you’re working with lots of simple equations all at once. It’s like moving from single variable calculus to multi-variable calculus. You realize that the additional complexity was there all the time, and you were just studying a special, restricted case before.
Yes, and it's super useful. The first times you find yourself working with several equations and you 'just' put that into a matrix form and solve that system is an amazing feeling of 'truth' having been hiding in plain sight.
Absolutely. It’s easy to forget how useful it is to be able to solve a system of equations like that. It lets you find optimal settings for complex systems with multiple constraints. Fitting a machine learning model is just one application for this... there’s a whole academic discipline called Operations Research that focuses on using optimization to find solutions to practical problems.
Just another example of the huge power in creating accurate digital models of the world.
Re: Introduction to Linear Algebra for Applied Machine Learning with Python
#13Earlier quoted context omitted.
Yes, and it's super useful. The first times you find yourself working with several equations and you 'just' put that into a matrix form and solve that system is an amazing feeling of 'truth' having been hiding in plain sight.
Absolutely. It’s easy to forget how useful it is to be able to solve a system of equations like that. It lets you find optimal settings for complex systems with multiple constraints. Fitting a machine learning model is just one application for this... there’s a whole academic discipline called Operations Research that focuses on using optimization to find solutions to practical problems. Just another example of the h…
We touched a bit of that. As an aside, when I was a student, we also had an applications module called "Numerical Analysis". We went through a bunch of algorithms (Cholesky, Seidel, Newton-Raphson, Gauss, etc.) and ran them by hand. We basically were "human computers". The exams were also solving problems using these algorithms, and given the iterative nature of many of them, if you make a tiny mistake it'll ripple and ruin everything for you.
As an aside, my background is in optimal control/control theory and instrumentation, and operational calculus, state space representations, and matrices were a huge part of the "Jiu-Jitsu" we did. Tinkering with RST control, robust systems, finding optimal systems and sequences (Hamilton-Jacobi-Bellman-Pontryagin) with matrices flying around on our exam papers solving these systems. It was a nice abstraction.
Very, very, powerful tools that command immense respect for Laplace, Lagrange, and people like them who invented things to solve problems we're facing now.
Re: Introduction to Linear Algebra for Applied Machine Learning with Python
#14Is there a website that anyone knows of for these types of open-source curriculums? Feel like it would be nice to have a place where people could post these and you could reference them when you wanted to learn something in the correct order and with the best resources.
Something like Kahn Academy (https://www.khanacademy.org/)?
Re: Introduction to Linear Algebra for Applied Machine Learning with Python
#15Is there a website that anyone knows of for these types of open-source curriculums? Feel like it would be nice to have a place where people could post these and you could reference them when you wanted to learn something in the correct order and with the best resources.
Something like Kahn Academy ( https://www.khanacademy.org/ )?
Khan Academy is great, but I mean for all resources on a subject. In other words, a place where people can post curations of resources, not actual content. So say I wanted to learn linear algebra it would point to Khan Academy for the basics part and then other places as well.
Re: Introduction to Linear Algebra for Applied Machine Learning with Python
#16Hi, I did that article :) https://twitter.com/CodeBug88 Saludos
Ola
Re: Introduction to Linear Algebra for Applied Machine Learning with Python
#17Earlier quoted context omitted.
Something like Kahn Academy ( https://www.khanacademy.org/ )?
Khan Academy is great, but I mean for all resources on a subject. In other words, a place where people can post curations of resources, not actual content. So say I wanted to learn linear algebra it would point to Khan Academy for the basics part and then other places as well.
Something like this https://github.com/rossant/awesome-math ?
Re: Introduction to Linear Algebra for Applied Machine Learning with Python
#18Is there a website that anyone knows of for these types of open-source curriculums? Feel like it would be nice to have a place where people could post these and you could reference them when you wanted to learn something in the correct order and with the best resources.
The list of "awesome lists" on github [1] is generally quite helpful (haven't checked them all myself obviously).
Re: Introduction to Linear Algebra for Applied Machine Learning with Python
#19Is there a website that anyone knows of for these types of open-source curriculums? Feel like it would be nice to have a place where people could post these and you could reference them when you wanted to learn something in the correct order and with the best resources.
For AI/ML, I think https://madewithml.com/ does the job. It has curated open source projects, courses, papers and topics.
Re: Introduction to Linear Algebra for Applied Machine Learning with Python
#20I was scrolling through to see if you explain how you typeset the math (notoriously hard on webpages), but I happened to instead find a small mistake. You write: "Elements of $\mathbb{R}^n$ are sets of real numbers." That is an incorrect definition.
- It is inaccurate because n doesn't enter into the definition (and thus all Euclidean spaces would be the same).
- You want ordered n-tuples, not sets. If you actually defined elements of R^n as sets of n real numbers, you would not be able to represent the diagonal (or, if you fix that, not be able to represent the difference between certain points on the diagonal of R^n and certain points on the diagonal of certain subspaces).
Moreover, figure 5 talks about "overlapping vectors". This is highly non-standard, and definitely would need to be defined.
Further, you're setting your readers up for trouble by defining vector arithmetic in terms of bases.