/sci/ - Science & Math

>>11708110
>the dimension
If you have m and n dimensional vector spaces [math]V, W[/math] over a field [math]k[/math], you can show [math]\mathfrak{b} = \{ v_i \otimes w_j \ |\ v_i\in \mathfrak{b}_V, w_j\in \mathfrak{b}_W\}[/math] is a basis for [math]V\otimes_k W[/math] whenever [math]\mathfrak{b}_V, \mathfrak{b}_W[/math] are bases of [math]V, W[/math]. Doing a bit of counting, we get [math]| \mathfrak{b}| = mn[/math], so the dimension is the product of the dimensions. Obviously, this generalises to any finite tensor product of finite dimensional vector spaces.

If your roots are real, then why is [math]z = e^{i\frac{\pi}{12}} \not\in \mathbb{R}[/math] but [math]z^{24} = 1[/math]? :^)

P.S. do you ever get spooked by your email beeping? That just happened to me.

>>11618016
Show those problems who's the boss! If you make another video, I'll check that out in the morning. Have fun!

Good night /mg/