Matt Pressland

5,369 reputation

1235

bio	website	people.bath.ac.uk/mdp33
	location	Bath, United Kingdom
	age	23
visits	member for	1 year, 3 months
	seen	yesterday
stats	profile views	436

Postgraduate student at the University of Bath, UK, studying geometry and representation theory. Currently thinking about cluster algebras and related objects.

	5,369 reputation	bio	website	people.bath.ac.uk/mdp33	visits	member for	1 year, 3 months
1235 badges		location	Bath, United Kingdom		seen	yesterday

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Apr 5	revised	Why $\operatorname{Hom}_A(e_jA, e_iA) \cong \operatorname{Hom}_A(e_jA, e_i\text{rad}A)$? added 60 characters in body; edited title
Apr 4	comment	*Name of $ab=c$ and $ba=-c$* @Lord_Farin That sounds like a reasonable guess at what was meant (and it would usually be written $ab=-ba$, to avoid unnecessary $c$s).
Apr 4	comment	*Name of $ab=c$ and $ba=-c$* I don't understand condition (1). What is $c$? It will always be true that $ab=c$ for some* $c$, so are you saying that $b*a=-a$ for all $b$?
Apr 4	comment	Proof of homeomorphism. A point of minor pedantry; there is not a unique homeomorphism $g\colon[0,1]/\sim\to S^1$, but there is a unique one such that $g([x])=f(x)$ (where $[x]$ denotes the equivalence class of $x$ under $\sim$).
Apr 3	comment	Formal Proof that area of a rectangle is $ab$ @Lord_Farin Fair enough, I hadn't thought of that loop. That almost suggests that the sensible thing to do is to define the area of a rectangle to be the product of lengths of sides, but one would hope that this is equivalent to some other natural definitions of area.
Apr 3	comment	Formal Proof that area of a rectangle is $ab$ It will also depend on what your definition of area is; if $a$ and $b$ are integers then you can do it by counting boxes as @SammyBlack suggests, but you could also use integration for example (although if you're starting from Euclid, this would be a lot of work).
Apr 1	answered	Cayley's Theorem quick question: examples of groups which aren't symmetric groups.
Apr 1	revised	Question on linear algebra-matrices deleted 12 characters in body
Mar 17	revised	How to prove one-one and onto? deleted 10 characters in body
Mar 15	comment	Invertability of a linear transformation A couple of pointers: it is not true that the sum of invertible linear transformations is invertible. For example, try the identity map and multiplication by $-I$. A smaller point is that you shouldn't really say "the" matrix representing $T$, but "a" matrix representing $T$, as the matrix depends on a choice of basis (although the properties you are checking do not).
Mar 15	comment	Confused on group notation Assuming usual notational conventions, it does indeed mean $\mathbb{Z}\times\mathbb{Z}$.
Mar 14	comment	Proof by contradiction: $ A \subseteq A $ It's fine, this is just a semantic argument anyway. Different people will find different notation clearer.
Mar 14	comment	Proof by contradiction: $ A \subseteq A $ That is also reasonable. My feeling to a degree though is that the contradiction arises from the fact that when you write $x\in A$, you can't tell "which $A$" you mean - you have to mean both - so you can't possibly also have $x\notin A$.
Mar 14	comment	Proof by contradiction: $ A \subseteq A $ I don't think I agree. This just encourages you to believe that things are different when they are actually the same. The contradiction is clearer if you write "$x\in A$ and $x\notin A$" than if you write "$x\in A_1$, $x\notin A_2$ and $A_1=A_2$". But maybe there are other reasons to prefer this notation.
Mar 14	comment	“The notion of an affine algebraic set is still not satisfactory” A comment because it's a vague, partial answer: the problem in question 2 is that in the case of $V(Y)\cap V(X^2-Y)$ there are "supposed" to be two intersection points, because you're intersecting a quadratic curve with a line, but the geometry says there is one, exactly like the intersection of two lines. You want some notion of multiplicity of intersection, so that you can rigorously say that the intersection point is really two points on top of each other.
Mar 14	comment	The Petersen Graph and its isomorphisms @kalpeshmpopat No. It seems you are misunderstanding something here. If you tell us exactly what your definition of a graph is, and what your definition of two graphs being isomorphic is (and start being a little more polite to people who are using their free time to help you), then somebody here can probably help you overcome this misunderstanding.
Mar 14	comment	The Petersen Graph and its isomorphisms @kalpeshmpopat You should look up what isomorphism means for graphs, and then think about the question again.
Mar 13	comment	If $H$ is a subgroup of $G$ and $x,y\in G$, what is $xHy$ called? It appears that whatever you call them, it should not be double coset (although it sounds like a sensible name) because this already refers to sets of the form $HxK$ for two subgroups $H,K$ and an element $x$.
Mar 13	comment	Can this product be written so that symmetry is manifest? The formula looks reminiscent of the McMahon formula for counting plane partitions (although it is genuinely different), which is also a function of three variables invariant under permutations of the variables. However in that case the invariance is clear either from the formula or the properties of plane partitions. Perhaps there are ways of rewriting the McMahon formula that carry over to your example and make it look more symmetric. Alternatively, it would also be nice to say that these values count objects such that the number of objects is clearly invariant under permuting $i,j,k$.
Mar 13	comment	A sort of inverse question in topology If you pick any topology on $Y$, then there is a smallest topology on $X$ such that the $g_i$ are all continuous (the one generated by all preimages of open sets in $Y$ under the $g_i$). As Cameron points out, there may then be extra continuous functions between $X$ and $Y$. What isn't immediately clear to me (but I'd be interested to know) is what conditions you need on the set $\{g_i\}$ such that this doesn't happen; this could easily depend on the choice of topology for $Y$. Alternatively, are there conditions on the $g_i$ giving a unique topology on $X$ and $Y$ so they're continuous.