Distributions 7 | Distributions Form a Vector Space

[@LopserGaming]

Amazing channel! I’m a graduate engineer and I feel that so many fundamental topics in mathematics have been skipped and this channel is helping fill in the gaps for the basics for many applications!

[@Duskull666]

Yes! Thank you for continuing this series! It has been very helpful in understanding my signal processing course, where they just dump on you alot of stuff from distribution theory (without explaing how they work or where they come from of course).

[@mathjitsuteacher]

Another great video!!! Thanks for continuing this series, it is hard to find good videos about this topic.

[@LeaoDN]

Wow, distribution theory is back and strong! Thanks for putting this together.

[@Hold_it]

Thank you for continuing this series :)

[@brightsideofmaths]

Glad you enjoy it!

[@zoedesvl4131]

My way of understanding distribution is basically as follows: if we "pretend" that integration by parts is OK, then it is OK.

[@coulsonyu7658]

the compatibility of two scalar multiplication and two addition is also can be called the preserving of algebric structure. Here we can view distribution spaces as an extension space of locally Lebesgue integrable function space which preserving of algebric structure. is it right? Thanks for your wonderful videos

[@brightsideofmaths]

Yes, the algebraic structure is important but we have way more as well. Thanks for your support :)

[@mastershooter64]

woah nice, can they be infinite dimensional vector spaces? and can you apply all the functional analysis stuff on them?

[@brightsideofmaths]

Yes, you can and should :)

[@mastershooter64]

@@brightsideofmaths great! :)

[@Tsusjgsgsks]

thanks

[@soumyadas9896]

sir can u tell me if the collection of singular distribution forms a vector space . if yes than how?

[@brightsideofmaths]

This cannot be true because 0 is a regular distribution :)

[@soumyadas9896]

@@brightsideofmaths thanks.