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No. 10261
150 kB, 800 × 800
I was sure we already had a thread about math, but I can't find it in the catalogue. So here is a new one.

And I'll just start it off with a question that I have trouble finding a conclusive answer to:
In a vector space the subspace spanned by the rows is perpendicular to the kernel, it is also orthogonal to it; is there a difference between perpendicularity and orthogonality of subspaces?
This relates to: If I have brought a matrix into rref with Gauss-Jordan, I can simply read a basis for the column space from the first r pivot columns (r being the rank of the matrix) and I'm wondering if I can read something about the basis of the kernel from the remaining columns (or rows?).
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No. 10263
>is there a difference between perpendicularity and orthogonality of subspaces?
Isn't perpendicularity just for vectors, so it's just a special case of orthogonality?
>If I have brought a matrix into rref with Gauss-Jordan, I can simply read a basis for the column space from the first r pivot columns (r being the rank of the matrix) and I'm wondering if I can read something about the basis of the kernel from the remaining columns (or rows?).
I can't recall it correctly, but i think that's depends from your kernel
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No. 10273
>>10263
I eventually solved it, though I'm not sure it's the shortest path.
Perpendicularity and orthogonality is the same. You can say that two vector spaces V,W are perpendicular if all vectors v1,..,vn in V are perpendicular to all vectors w1,..,wm in W. Which is defined over the orthogonality derived from the dot product.

In that manner, the kernel of a matrix A is orthogonal to the row space of A. To find the basis of the kernel, I need to get the transpose of A into rref, thus finding the basis for the row space and from that I can also read the basis of the kernel.
With the regular rref I could only find out the basis of the "left kernel" (aka the kernel of the column space).
Found the answers in lecture 9 and 10 of MIT 18.06: https://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD91010BC51F8
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No. 10493
How does one go though a mathematics book in a (relatively) short amount of time?
Book somewhat related: http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf
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No. 10496
>>10493
Set yourself a time to hit every day and truck away at it. Even if it's just a half hour, you'll make good progress.
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No. 10524
>>10493
Another suggestion: Each time you run across something you can't understand within a reasonable time, write down what it is and what question you have about it and then move on. Then, a few days later (assuming you've continued to study in the mean time) you look at what you wrote down and there is a good chance it will just click. That way, you don't get stuck for hours, losing motivation.
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No. 10527
>>10493
>Schlomo
BTW is there a difference between European math and American (jew) math? Or is math the one subject in college that hasn't been corrupted
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No. 10528 Kontra
>>10527
This is a thread about mathematics, not political agenda. Please go back to Kohl if you can't tell the two apart.
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No. 10529 Kontra
>>10527
This is an amazingly bad post and you should feel bad. It's hard to even understand there's people this fucking dumb in the world.
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No. 10591
166 kB, 1024 × 810
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No. 10595 Kontra
103 kB, 1306 × 354
>>10591
This is a thread about fucking math piss off back to /pol/
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No. 10604
If you don't know the answer to the question about math then shut the fuck up or say "I don't know" no need to post your 4chan and Kohl drama on here. Most fall into "I've never taken math classes in EU/USA so I can't compare" "I use whatever books Merkel/Obama forced upon me"
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No. 10608 Kontra
>>10604
>"I use whatever books Merkel/Obama forced upon me"
>math textbooks
Please fuck off and don't come back
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No. 10623 Kontra
>>10608
They don't teach math right in America, anyone who got a Catholic education knows, or any immigrant
https://www.youtube.com/watch?v=b7A2ZM7MnDM