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.
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.
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.
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.
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.
brilliant video
This is a great video! Please keep these up. This is what math education should be, I think.
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.
It is indeed true.
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.
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.
Unbelivably great videos as always. Although I like this video a lot, my favorite one is still the "Cardinality of the Continuum" video 😊
Waiting for the next video. Bravo
Awesome video!!!
thank you so much 🤩🤩🤩. much better than class
This isn’t related to any of the math, but I’m glad to see C418’s non Minecraft music being used
Superb!
Great info but the muzak is distraction.