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Apr
30
awarded  Nice Answer
Apr
25
comment Products of positive definite matrices
@S.Panja-1729 I'm using the definition of a positive-definite matrix as given on wikipedia. According to this definition, each positive-definite matrix is symmetric. If, however, you choose to define positive-definite matrices as any matrices that have $x^T A x > 0$ for each column $x \neq 0$, then the statement in the question simply becomes false.
Apr
7
comment Let $H$ and $K$ be normal subgroups of $G$ such that $H \cap K = \langle e \rangle$ and $HK = G$. Prove that $G$ is isomorphic to $H \times K$.
@grayQuant no, it's not necessary here. When it's established that $\varphi$ is bijective and a homomorphism, then $\varphi$ is an isomorphism simply by definition.
Mar
17
revised Prove complements of independent events are independent.
added 566 characters in body
Mar
16
answered Prove complements of independent events are independent.
Mar
15
awarded  Organizer
Mar
15
revised Complete labeled Graph $K_6$ and Spanning Tree
edited body
Mar
15
comment Complete labeled Graph $K_6$ and Spanning Tree
I've already given a link to the Wikipedia article. I can't tell you anything on top of what you'll see there and/or find elsewhere on the Internet.
Mar
15
answered Complete labeled Graph $K_6$ and Spanning Tree
Mar
4
comment Finding two smallest composite numbers
Not that it's very important, since we don't want primes, but $2$ and $3$ also satisfy the congruences simultaneously.
Mar
4
comment Changing order of integration in a double integral
Does it really say $\sqrt{9-y}$ and not $\sqrt{9-y^2}$? It doesn't change anything important, but it looks a bit evil. Just saying.
Mar
4
answered Given a collection of functions $f_i$ with the same domain, how to replace with values (w/o axiom replacement)
Mar
4
revised discrete family of sets
latexify
Mar
4
comment discrete family of sets
What is your proof for the case when $F$ is finite? Do you really use the finiteness at all?
Mar
4
comment Hard Olympiad Proof Problem
Doesn't look like a complete proof. You've only proved that your particular family cannot be made larger by adding new intervals.
Feb
26
comment The ideals of $A \times B$ for fields $A,B$.are principal
First of all, you cannot show that $I \times J \subseteq \langle(a,b)\rangle$, as shown in quid's answer. Even more importantly, your plan has another flaw: you only consider ideals in $A\times B$ that can be decomposed into a direct product $I \times J$, where $I \subseteq A$ and $J \subseteq B$, but you actually need to consider arbitrary ideals in $A \times B$.
Feb
12
awarded  Nice Answer
Jan
14
comment Symmetric Group acting on $X \times X$
Not really sure what the question is... Why don't you look at $n=3$, find the orbits by hand, and then generalize?
Dec
21
comment Finding median of union of two sorted (ordered) lists
Your final comment seems a bit weird. I'd say that one can find the median of a sorted list in $O(1)$ (if the list is an array and we have instant random access).
Dec
20
awarded  Caucus