Linear Algebra 6 | Linear Subspaces

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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)

[@AJ-et3vf]

Great video! Thank you! This reminds me of powerful numerical method used to solve large sparse systems of linear equations: Krylov subspace methods.

[@VolumetricTerrain-hz7ci]

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!

[@hopelesssuprem1867]

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

[@brightsideofmaths]

Thank you very much :)

[@malawigw]

Finally!

[@mastershooter64]

ayyyy linear algebra is back! hello! up to what topics are you going to cover?

[@brightsideofmaths]

All of them :D

[@mastershooter64]

@@brightsideofmaths awesome :D

[@oni8337]

@@brightsideofmaths hoping for a rank nullity video :)

[@Stefan-dg2js]

Thanks, your explanations are so much better then the ones from my unmotivated math prof

[@brightsideofmaths]

Glad you like them!

[@DOROnoDORO]

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

[@legasalehlogonolo]

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 🎉✨❤‍🔥❤‍🔥❤‍🔥

[@brightsideofmaths]

Happy to help! :)

[@ichkaodko7020]

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?

[@brightsideofmaths]

Affine subspaces are not linear subspaces in general.

[@ichkaodko7020]

@@brightsideofmaths ah thank you. that's why affine subspace has no zero vector in it hence it is not linear.

[@narendraparmar1631]

Thanks

[@brightsideofmaths]

Nice :)

[@malawigw]

If I have a subspace, I will get a vector in you

[@L23K]

Warum nach meiner mathematischen Grundlagen Klausur :((