/math/ pls help

>>7956599
Have you even tried anything? This is mostly plug and chug

>>7956599

That's trivial. You don't see it? I feel bad you should reconsider your major.

>>7956850
>Have you even tried anything?
No. It looks really tedious, I don't want to do it.

>>7958455
/sci/ in a nutshell

>>7956599
Don't hate... but what's the [math]\circ [/math] on the right hand side? Obviously the left is composition, but what is it for spaces?

>>7959336
[math] Al{t^k}f [/math] is also a function.

[math] Al{t^k} [/math] is a contravariant functor,

[math] Al{t^k}:{\text{Mor}}\left( {V,W} \right) \to {\text{Mor}}\left( {Al{t^k}W,Al{t^k}V} \right) [/math]

>>7959343
To clarify, thats what it means when acting on a function.

When acting on a vector space, like V, it denotes the space of alternating k-forms on V.

>>7956599
you study at cambridge don't you?

>>7959336
If you aren't happy with functors, just know that you can apply Alt to a vector space and get a vector space, or to a linear map and get a linear map. The latter is what is being done here.

>>7959376
no

this is where I don't even bother with math
it's just nonsense
just learn enough linear algebra to do useful stuff like tensor strength and optimization shit
this tedious nonsense is just autistic circlejerking
not relating to anything

>>7961836
Man, it's one thing to read of these opinions when regular people write, but it's depressing when people who can even understand linear algebra, which admittedly is extremely little, still aren't respectful of abstract thought or advanced science.

Anyway, OP the first problem is standard functoriality of the exterior power of a vector space. Part c is just standard expansion of the determinant given a and c, as the question suggests.

>>7961836
This is the same attitude you people deride humanities students for taking towards math and science. Have a little intellectual curiosity.

>>7961867
pfff

http://arxiv.org/pdf/1305.0644.pdf

>>7961836
>>>/hm/

>>7963234
Very nice.

The "permuted indices" based definition of determinant is bad enough. I have zero intuition for the Cauchy-Binet formula.