Linear Algebra 6 | Linear Subspaces

Thanks to all supporters! They are mentioned in the credits of the video :)

This is my video series about Linear Algebra. I hope that it will help everyone who wants to learn about it.

#LinearAlgebra
#Vectors
#Matrices
#MachineLearning
#Eigenvalues
#Calculus
#Mathematics
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(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-etvf]

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

[hopelesssuprem]

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

[mastershooter]

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

[Stefan-dgjs]

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

[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 🎉✨❤‍🔥❤‍🔥❤‍🔥

[VolumetricTerrain-hzci]

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!

[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

[malawigw]

If I have a subspace, I will get a vector in you <3

[ichkaodko]

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?

[LK]

Warum nach meiner mathematischen Grundlagen Klausur :((