Abstract vector spaces | Chapter 16, Essence of linear algebra
Video Statistics and Information
Channel: 3Blue1Brown
Views: 896,014
Rating: 4.9821653 out of 5
Keywords: blue, vector space, 3brown1blue, math, 3 brown 1 blue, one, abstract vector space, three, 3b1b, brown, linear algebra, three brown one blue
Id: TgKwz5Ikpc8
Channel Id: undefined
Length: 16min 46sec (1006 seconds)
Published: Sat Sep 24 2016
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This series is the gold standard of educational math videos.
The "rules" of vector spaces seemed to relate in a weird sense to group theory and the "rules" of groups, fields, and rings. Can anyone help me see this connection more concretely?
Such an awesome series! Thanks for the great work, /u/3blue1brown!
As for the message at the end, like I like say, Ceci n'est pas un vecteur!
He didn't say this explicitly, but it's worth noting that ANY (finite dimensional) "abstract" vector space (using the field of real numbers) is isomorphic to Euclidean space (Rn ). So you can come up with any whacky vector space and describe linear transformations on it with a matrix of real numbers.
I guess word2vec could be a cool example of one such "abstract vector space"?
I hope I get to TA an Intro to Linear Algebra course soon because I'm going to push this series heavily.
This was a beautiful final video for the series. It all makes so much sense now!
As much as I love linear algebra now, I remember my first year linear algebra course defining a vector space in the 2nd or 3rd lecture. It seemed like a joke... entirely unmotivated.
When I finally understood it's purpose (taking the common properties of euclidean vectors and functions into a unified abstract framework), it was like a revelation, but that didn't come until long after the course was already done.
I'm glad this video explains things the right way, starting with the concrete and building to the abstract.
really liked this video, good insperation for someone 3 weeks in to solving boring systems of equations