Linear Algebra 6 | Linear Subspaces
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- Опубліковано 12 тра 2022
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This is my video series about Linear Algebra. I hope that it will help everyone who wants to learn about it.
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x
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
Great video! Thank you! This reminds me of powerful numerical method used to solve large sparse systems of linear equations: Krylov subspace methods.
Finally!
This is the best explanation of linear algebra I've ever seen. By the way english is not my native language but I understand everything
Thank you very much :)
There are unknown way to visualize subspace, or vector spaces.
You can stretching the width of the x axis, for example, in the right line of a 3d stereo image, and also get depth, as shown below.
L R
|____| |______|
TIP: To get the 3d depth, close one eye and focus on either left or right line, and then open it.
This because the z axis uses x to get depth. Which means that you can get double depth to the image.... 4d depth??? :O
p.s
You're good teacher!
the only reason i failed linear algebra last year was that i didnt met your youtube channel. thank you very much for your explanations, this year i feel distinction 🎉✨❤🔥❤🔥❤🔥
Happy to help! :)
I thought of an interesting example: is {(x, y) | xy ≥ 0} a subspace of R²? It's the union of the first and third quadrant.
edit: nope, (1, 3) + (-2, -1) = (-1, 2) which is not in that set. rip
ayyyy linear algebra is back! hello! up to what topics are you going to cover?
All of them :D
@@brightsideofmaths awesome :D
@@brightsideofmaths hoping for a rank nullity video :)
If I have a subspace, I will get a vector in you
Thanks, your explanations are so much better then the ones from my unmotivated math prof
Glad you like them!
Thanks
Nice :)
I am wondering if affine subspace is indeed a subspace? I mean, by the characterisation for subspaces, no zero vector is in affine subspace right?
Affine subspaces are not linear subspaces in general.
@@brightsideofmaths ah thank you. that's why affine subspace has no zero vector in it hence it is not linear.
Warum nach meiner mathematischen Grundlagen Klausur :((