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 Apr 11 awarded Popular Question Feb 23 revised How do I show this matrix is rank deficient? added 1 character in body; added 1 character in body Feb 23 asked How do I show this matrix is rank deficient? Nov 25 awarded Tumbleweed Nov 18 asked Connection between maximizing a quadratic form and maximal variance Nov 18 asked Intuition for the singular vectors and the outer products in SVD of a non-diagonalizable matrix Nov 17 comment Difficulty understanding proof of Yoneda's Lemma I was just reading about this part today. Yoneda functor. I can follow the arrows but I'm still not as comfortable as id like bookkeeping in my head the appearance of the natural transforms because of the layering (arrows on sets of arrows). I'll keep at it. Nov 17 asked Understanding representable functors Nov 15 comment What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices? got it, thanks! Nov 15 comment What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices? Jack, how do you get the $j!$ in ${k\brace j}\cdot j!\cdot\binom{n}{j}$? I was reading this as choose the $j$ unique drinks in ${n \choose j}$ ways then for each of those you have $k$ people and you want to partition them into $j$ non-empty sets (stirling of second kind) which is ${k \brace j}$ but I don't see where $j!$ comes in... Nov 15 accepted What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices? Nov 15 comment What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices? Yes! This agrees numerically in R with the $M^{k-1} \cdot 1:k^t$ Nov 15 comment What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices? You're right, in that case it's not straightforward to me how to express an exact probability for $i$. Nov 15 revised What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices? added 172 characters in body Nov 15 asked What is the expected number of distinct drink types a group of $k$ people will order if there are $n$ choices? Nov 15 comment Difficulty understanding proof of Yoneda's Lemma Nov 15 revised Difficulty understanding proof of Yoneda's Lemma deleted 235 characters in body Nov 15 revised Difficulty understanding proof of Yoneda's Lemma deleted 235 characters in body Nov 15 comment Difficulty understanding proof of Yoneda's Lemma It kinda helps to think of $\Phi$ as a collection of maps, yes. And I understand how by defining $\Phi_A$ on (the map between $Hom(A,A)$ and $F(A)$) on $id_A$ we fully establish $\Phi_X$ (the map between $Hom(A,X)$ and $F(X)$) for any $f$. What I'm trying to do now is see if this gets us a commutative square involving $Hom(A,X), Hom(A,Y), F(X)$, and $F(Y)$ Nov 15 comment Difficulty understanding proof of Yoneda's Lemma I don't know how either, I think I've updated my question to agree with your Point 2. $f_*(id) = f$ is true, yes. I think what I don't get is $\Phi$ - it's some "higher level" abstraction so I'm having trouble extending the logical consistency of the inner square above to arbitrary $X,Y$ and visualizing all of $\Phi$