Quotient Space (+ Pics, Properties & Proofs)

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I explain the translation of a linear subspace by a vector. The space that contains all parallel-translations of a subspace, is called quotient space. I show you some important properties and prove them!
Translation of subspaces (0:20)
a + U = b + U criterion & proof (4:22)
Quotient V/U (10:47)
Quotient Space V/U (12:53)
Dimension of V/U & Proof-Sketch (15:57)

*I am sorry for any incorrect pronunciation of English words*

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Комментарии

Best explanation for quotient space on yt. Thanks a lot Sir.

monicabrasow

I have uploaded a new video, where I prove the rank-nullity theorem using results about quotient spaces from this video.

forty-moo

Thank you. Your video help a lot! There is very few video about quotient space on YouTube.
I was having difficulty on understanding torus as a quotient space. Your video help me get some basic about quotient space.
I think if you can add some examples about typical quotient spaces, such as torus, people would get more intuition of what quotient space can achieve.

davidtan

Thank you for your great explanation. There is only a little mistake in the visualization of the subtraction of vectors (b-a). The resulted vector should be placed in U, and not in a+U. Check it in 10:28

AliHasanAli

Hi what will be the kernal for these quotient space

a.shakila

Can you explain how to show that elements b_k+1 + U, ..., b_n + U form a basis of V/U?

razbenhaim

THANK YOU
BUT IF YOU FINISH PROOFING THE DIMENSION THAT WILL BE GREAT

g-abeshawel

that circle shit every time you click is incredibly annoying especially when you click every second

zwan

Quotient Space (+ Pics, Properties & Proofs)

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