A wonderful and intuituve explanation of such concepts. As an engineering student who is curious about mathematics I am glad that you decided to dedicate a playlist for linear algebra. I hope you post more advanced topics about it soon:)
@zyugyzarc4 ай бұрын
This explanation makes a LOT more sense - that span(M) is a subspace in R^n
@Leslie.Green_CEng_MIEE2 ай бұрын
In example (a) at 3:59, u is given as an element of R^n. Given that the example is in R², and that the span is the smallest subspace with the required property, I would have started from u being an element of R². Clearly the RHS gets reduced/simplified on the next line(s), so it is probably not important.
@brightsideofmaths2 ай бұрын
Thanks! Yes, it's a typo. n =2 in this case :)
@punditgi2 жыл бұрын
Glad to see another one of your videos! 😃
@brightsideofmaths2 жыл бұрын
Hope you enjoyed it! :)
@kirikouestpetit65432 жыл бұрын
Thank you so much for these ! A friend recommended your channel to me last summer and I've been binging your videos ever since. I started a college math heavy course as someone who used to be terrified of maths. You and some other channels made me love them :-) I am so grateful and someday I hope to be able to contribute a bigger amount to your channel monthly. Maybe I missed them but do you ever plan on covering dedekind cuts ? We're studying them right now, along with "ideal polynomials" (if that is the term in English...), would be curious to see your take on it. :-) Great work !❤
@user-gm3pk5cp3z Жыл бұрын
Why haven't I discovered this cannel before ? vielen danke
@brightsideofmaths Жыл бұрын
Thanks! I hope you can use the channel now :)
@Hold_it2 жыл бұрын
Great video. Keep up the good work👍
@GeoffryGifari2 жыл бұрын
is it possible to assign equality to span{ }? from your example of span{ (1 0 0), (1 1 0)} being the entire XY plane, i imagine span{(1/2 0 0), (0 1/2 0)} is also the XY plane, so many sets of vectors can span a set equally
@brightsideofmaths2 жыл бұрын
Yes! Different vectors can span the same subspace!
@GeoffryGifari2 жыл бұрын
and also, is it *not* possible to find the *largest* scalar with which we can multiply the vectors of set M when we're making span{M} ? (so that one ray built from one of our vectors don't extend forever) i see that if this is the case its not possible to have a span inside a closed, finite area in R² for example (like the blob drawn early in the video)
@brightsideofmaths2 жыл бұрын
Yes, the span is always a subspace, which cannot be a finite area in R^2.