But what is a Vector Space?

[@davidwright8432]

Many thanks! I'm giving myself a refresher, from the beginning, of stuff I 'learned' as an undergrad - a while back! Now it's all beginning to make sense - not just a way of doing problems by routine.

[@aidsan6950]

This is a great video! Please keep these up. This is what math education should be, I think.

[@angeldude101]

Something I love about vector spaces is that... who said scalars aren't themselves vectors?🙃 If you want to be technical, it's possible to argue that ℝ is itself a vectorspace over the field ℝ, and, thinking about abstraction, the same should probably be true for any field.

[@adityaruplaha]

It is indeed true.

[@Happy_Abe]

And to abstract this a bit more, any field K is a vector space over any subfield F in K. The size of its basis over a subfield is what is known as the degree of the field extension from F to K. This is a huge concept in field theory and Galois theory.

[@quantumgaming9180]

Unbelivably great videos as always. Although I like this video a lot, my favorite one is still the "Cardinality of the Continuum" video 😊

[@dailymemigzugxoyditsi3273]

Brilliant 🎉 video. I would like to make a suggestion, that being a video on tensor just like this having axiomatic definition. The reason I request is most of us students are clueless about what tensors is in mathematical stand point.

[@aincrad6383]

brilliant video

[@martinsanchez-hw4fi]

Waiting for the next video. Bravo

[@JJ-tp2lc]

This isn’t related to any of the math, but I’m glad to see C418’s non Minecraft music being used

[@defango]

Awesome video!!!

[@mohamedmouh3949]

thank you so much 🤩🤩🤩. much better than class

[@modolief]

Superb!

[@54johndavis]

Great info but the muzak is distraction.