Let $F$ be a field of characteristic 0. Let V be a finite dimensional over F. Suppose that $ E_{1},...,E_{k}$ are projections of V and that $E_{1}+...+E_{k}=I$. Prove that $E_{i}E_{j} = 0$ for $ i \ne 0$. Please help
@Abcd Kinetics and thermodynamics are kinda separate most of the time. Back in my undergrad, we are being taught thermodynamics before kinetics. It is more important to understand chemical equlibrium first before dealing with kinetics, as concepts like gibbs free energy is needed to make sense of kinetics
Let F be a field of characteristic 0. Let V be a finite dimensional vector space over F. Suppose that E1,E2,...,Ek are projections of V and that E1+E2+...+Ek = I (Identity operator). Prove that Ei . Ej = 0 for i not equal to j. Please help.
@KasmirKhaan if we are finding the $f_{net}$ using the equation $F_{net}=ma$ and our mass is $2.75$kg and our acceleration is $4$ m/s. Do we write the $F_{net}$ as kg/ms?
When you ask a follow-up question 2 hours ago, see that the guy has edited his answer with something that has nothing to do with your follow-up question 1 hour ago, and completely ignores you.
Eisenstein devised a geometric proof in order to prove quadratic reciprocity. I want to see a non geometric proof. And not one thats mod 2 either. Sum[Floor[(q k)/p], {k, 1, (p - 1)/2}] + Sum[Floor[(p k)/q], {k, 1, (q - 1)/2}] == (1/4) (p - 1) (q - 1) /; Element[p, Integers] && Element[q, Integers] && p > 0 && q > 0 && GCD[p, q] == 1
let $F$ be a field of characteristic 0. Let $V$ be a finite dimensional vector space over $F$. Suppose $E_{1},E_{2},...,E_{k}$ are projections of V and that $E_{1}+E_{2}+..+E_{K}=I$. Prove that $E_{i}E_{j} = 0$ for $i \ne j$.Please help.
@TedShifrin let $F$ be a field of characteristic 0. Let $V$ be a finite dimensional vector space over $F$. Suppose $E_{1},E_{2},...,E_{k}$ are projections of V and that $E_{1}+E_{2}+..+E_{K}=I$. Prove that $E_{i}E_{j} = 0$ for $i \ne j$.Please help.
@TedShifrin I don't understand that hint but all you wanted me to prove was that the etale space of the sheaf of holomorphic functions on $\Bbb C$ is Hausdorff, didn't you?
@NV-US Multiplying $E_1$ and using the fact that projections are idempotent, you obtain $E_1 E_2 + \cdots + E_1 E_K = 0$. Repeat for other $E_i$ and you're done.
@NV-US Multiplying $E_1$ and using the fact that projections are idempotent, you obtain $E_1 E_2 + \cdots + E_1 E_K = 0$. Repeat for other $E_i$ and you're done.
@TedShifrin you obtain $E_1 E_2 + E_1 E_3=0$, $E_2 E_1 + E_2 E_3 = 0$, and $E_3 E_1 + E_3 E_2 = 0$, and you can flip all the products in every sum. Hmm, you're right, I can't make the orders match.
So I have this map $p : |\mathscr{O}(\Bbb C)| \to \Bbb C$. To prove it's not a covering space, suffices to show that for a point $z_0 \in \Bbb C$ there is no neighborhood $U$ around $z_0$ so that $p^{-1}(U)$ can be written as a disjoint union of open sets around the germs at $z_0$.
@Jasper Things with me are simple, as before: working very hard, excepting now when I talk to you, that means I took some break (which I deserve I think).
