meta user
network profile
| bio | website | abclinuxu.cz/blog/Arcadia |
|---|---|---|
| location | Prague, Czech Republic | |
| age | 27 | |
| visits | member for | 2 years, 6 months |
| seen | May 13 at 17:52 | |
| stats | profile views | 496 |
Programmer and theoretical physicist with an eye on studying algebraic geometry.
Currently I am getting familiar with the basics of number theory, classical varieties and the commutative algebra underlying them. My other interests include anything involving geometry and groups (differential topology, algebraic topology, representation theory, etc.).
|
Jun 19 |
comment |
Draw a 3D parametric curve You can draw the curve even without the collected information. Just take $t=0$, $t=0.1$, ..., compute $\gamma(t)$ and put down a point there. Or if you are familiar enough with trig functions you might even guess how the result will look like. |
|
Jun 19 |
answered | What is the relationship between the Boltzmann distribution and information theory? |
|
Jun 18 |
answered | Functions as integrals of basis functions |
|
Jun 18 |
answered | Why is $SO(3)\times SO(3)$ isomorphic to $SO(4)$? |
|
Jun 18 |
comment |
How to partial differential of a trace of matrix form? Hint: write out the definitions of matrix product, trace and partial differentiation in full. The rest is straightforward calculation. |
|
Jun 18 |
comment |
if $s \implies \lnot w$, does $\lnot s \implies w$? As for the question in the title: no, it doesn't. As for the question in the body, I don't follow at all. What does (5) have to do with anything? In particular, as you have already deduced $\lnot s$, (5) plays no further role in any deduction (besides possibly deducing a contradiction, but that's not the case here either). |
|
Jun 18 |
comment |
Proving that two systems of linear equations are equivalent if they have the same solutions Any reason for working in two dimensions and writing out all the solution cases? In my mind the general proof is as simple as this: let $W$ be the solution space and $W'$ its orthogonal complement. Define a matrix $C$ that acts as identity on $W'$ and annihilates $W$. Now, by Gauss elimination, both $A$ and $B$ can be brought into this form and therefore are equivalent to $C$ and therefore to each other. |
|
Jun 18 |
comment |
Find the limit $\lim \limits_{n\to \infty }\cos \left(\pi\sqrt{n^{2}-n} \right)$ @Nir: it is very important that $n$ here is integer. |
|
Jun 18 |
comment |
Integral question: $\displaystyle\int \frac{x^{n-2}}{(1 + x)^n} {\rm d}x$ @Jaydon: thanks. And by the way: me neither, up until now :) The main point is that you want to get rid of annoying terms like $(x / (1+x))^n$ and transform them into something simple that you know how to deal with. By using substitution we might have produced a complicated expression due to differentiation (indeed, that the result here is so simple is just a coincidence) but at least we isolate the hard power part into one simple $y^n$ term. |
|
Jun 18 |
answered | Integral question: $\displaystyle\int \frac{x^{n-2}}{(1 + x)^n} {\rm d}x$ |
|
Jun 18 |
comment |
Join of simplices and spheres "This should be homeomorphic to a sphere with 2 points removed, so it should be again homeomorphic to a sphere." -> You must be talking about some other definition of homeomorphic than the one I am familiar with because sphere with two points removed is a cylinder in my book, not a sphere... |
|
Jun 18 |
comment |
Finding a basis for a submodule Do you understand what a basis of a module is? Also, how did you manage to find $d_1$, $d_2$, $d_3$ if you can't even find the basis? |
|
Jun 18 |
comment |
Evaluating $\lim_{x\to \infty}\sqrt[6]{x^{6}+x^{5}}-\sqrt[6]{x^{6}-x^{5}}$ @Américo: use the binomial formula. For the second term you'll get $6x^5 ({1\over 6}) = x^5$. So just work in reverse. The idea is similar to completing a square... |
|
Jun 18 |
comment |
Proving that two systems of linear equations are equivalent if they have the same solutions @Lundmark: here it is probably an equivalence relation on the matrices associated with the equations, defined by some row/column operations. So the thing to prove is that those operations don't change the solution space. Is this what you had in mind, @Herman? |
|
Jun 16 |
comment |
Quick way to find the number of the group homomorphisms $\phi:{\bf Z}_3\to{\bf Z}_6$? For anyone wondering what is a ring function such as $\rm gcd$ doing in group theory: it might be useful to recall that every abelian group is actually a $\mathbb Z$-module. |
|
Jun 14 |
comment |
Solving for the implicit function $f\left(f(x)y+\frac{x}{y}\right)=xyf\left(x^2+y^2\right)$ and $f(1)=1$ @Thomas: ah, that is indeed neater. |
|
Jun 14 |
comment |
Morphisms in the category of natural transformations? Indeed, good points. |
|
Jun 14 |
answered | Solving for the implicit function $f\left(f(x)y+\frac{x}{y}\right)=xyf\left(x^2+y^2\right)$ and $f(1)=1$ |
|
Jun 12 |
comment |
The motion of a system as a level set of the energy @dissonance: you're welcome. |
|
Jun 12 |
revised |
Independence of sums of gaussian random variables Fixed typos, added formatting |
