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comment Why might André Weil have named Carl Ludwig Siegel the greatest mathematician of the 20th century?
I once heard from someone who claims to have been present that Weil in fact hesitated before naming Siegel, and that when he was asked "And who is the second greatest?", Weil replied without hesitation "Myself, of course". I have no idea whether any of this is accurate, and of course even if it's accurate I have no idea in what tone, and with what non-verbal expressions, the answer was delivered, which could make all the difference in how it should be interpreted.
Aug
18
comment Does every projective A/I-module come from A?
Notice that your exact sequence (some version of which does exist per Mariano's answer) is far from sufficient to establish your claim. Surjectivity of $K_0(X)\rightarrow K_0(Z)$ is far from sufficient to establish that every $Z$-projective lifts to $X$.
Aug
14
comment Meaning of $[A,B]$ when $A$, $B$ are self-adjoint
Actually, the paper you link to (in the answer you link to) denotes the non-standard Lie bracket $(A,B)$, not $[A,B]$.
Aug
11
comment Meaning of $[A,B]$ when $A$, $B$ are self-adjoint
@RobertBryant: This sounds like it is probably the answer I'm looking for --- though, because there are two possible non-standard usages, I'd still like to know whether one is generally preferred to the other.
Aug
11
comment Meaning of $[A,B]$ when $A$, $B$ are self-adjoint
@RobertBryant: Thanks for this --- but I'm not sure it answers the question. In a math paper, is it less confusing to use $[A,B]$ for the commutator, or for the Lie bracket, or ought one not use this notation at all?
Aug
11
asked Meaning of $[A,B]$ when $A$, $B$ are self-adjoint
Jul
23
revised Worst case difference in rank by column-row swapping
added 184 characters in body
Jul
23
comment Worst case difference in rank by column-row swapping
@BrendanMcKay: Actually, I'm back to not being sure what "swapping" means, so the operation might be as in my comment or as above. Fortunately, the above argument works either way. I've included an edit to mention this.
Jul
23
revised Worst case difference in rank by column-row swapping
edited body
Jul
23
revised Worst case difference in rank by column-row swapping
deleted 366 characters in body
Jul
22
comment Worst case difference in rank by column-row swapping
I've deleted my last comment, which was nonsense.
Jul
9
revised the true reason of the incompleteness of formal systems
added 610 characters in body
Jul
9
comment Worst case difference in rank by column-row swapping
@BrendanMcKay: The operation seems to be $$\pmatrix{A&B\cr C&D\cr}\mapsto \pmatrix {A&C^T\cr B^T&D\cr}$$ where $A$ and $D$ are square matrices (perhaps of different sizes), $C$ and $D$ are rectangular of appropriate sizes, and the upper-$T$ denotes the transpose.
Jul
9
revised Worst case difference in rank by column-row swapping
added 107 characters in body
Jul
9
revised Worst case difference in rank by column-row swapping
added 17 characters in body
Jul
9
answered Worst case difference in rank by column-row swapping
Jul
7
awarded  Good Answer
Jul
5
comment Which journals publish research announcements?
@SergeiAkbarov: A "research announcement" is a short communication without complete proofs.
Jul
5
comment Worst case difference in rank by column-row swapping
Ah. I see that you've changed your example to respond to my last comment, but without bothering to mention or acknowledge it.
Jul
5
comment Worst case difference in rank by column-row swapping
Your example adds to my confusion. If $S_i$ is the operation that "swaps" the $i$th row and column, and if I understand what "swap" means, then it seems that the $S_i$ commute with each other. But your example suggests that the results of applying $S_iS_j$ and $S_jS_i$ are different. So I'm back to believing that I don't know what "swap" means.