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seen Jun 29 at 20:11

Jul
2
awarded  Curious
Jun
12
answered Linearity of $D_{v}f(0)$
Jun
12
comment Linearity of $D_{v}f(0)$
Right, but for a linear function, you could easily generalize your calculation (just write $f(v) = cv$ for some $c$; the result is given in the answers, really).
Jun
12
comment Application of Riemann Roch
When a reference is abstract is probably dependent on who you are, but the result you're mentioning is Corollary 16.12 of Forster's book "Lectures on Riemann Surfaces" which is fairly concrete.
Jun
12
comment Linearity of $D_{v}f(0)$
Do you know the theorem saying that differentiability is implied when partial derivatives exist and are continuous around the point in question?
Jun
12
comment The normal of a surface that passes through the origin
The only point $(x,y,z)$ satisfying $x^2+y^2+z^2 = 0$ is $(0,0,0)$.
Jun
12
answered P3 being subspace of vector space?
Jun
11
comment what type of functions has $f(x+y) \geq f(x) + f(y)$
For the first question: no. There are real functions $f$ satisfying $f(x+y) = f(x)+f(y)$ with dense graph.
Jun
10
comment Question about $e^T$ where T is a transformation
For the first part, the diagonal $2 \times 2$-matrix with entries $2$ and $1$ has determinant $2$ but its exponential has determinant $e^2 \cdot e = e^3$.
Jun
5
comment Help clarify truth of the statement: $n^2-n-2=0 \Leftarrow (n=2 \text{ and } n=-1)$
Yeah, it happens to also be true with "and" replaced by "or", so it looks like a trick question.
Jun
3
comment Geodesics intersection on a cylinder
Not quite: in the cylinder case, the geodesics are exactly the helices. So, suppose for instance that the two points lie on a vertical line. Then one geodesic would be simply that vertical line, but you can also imagine a helix connecting the two points (in fact, infinitely many helices will do so). Now of course, you could simply restrict attention to the shortest among all geodesics and ask your question for those. Maybe that's what you want?
Jun
3
comment Prove $\mathbb{R}^n$ and $\mathbb{R}^m$ are not topologically equivalent spaces.
Do you know about Brouwer's invariance of domain theorem?
Jun
3
comment Geodesics intersection on a cylinder
Hmm, given two points on the cylinder, there will be infinitely many geodesics connecting them.
May
28
comment Calculating a basis in $\mathbb{R}^4$.
A basis for $\mathbb{R}^4$ always has four vectors, sure, but in this case, you want a basis for $W$ which is a $3$-dimensional hyperplane in $\mathbb{R}^4$.
May
27
comment Group of distances
If $g_1, g_2 \in G$ with corresponding integers $n_1$ and $n_2$, then $g_1 \circ g_2$ satisfies the condition defining $G$ with $n = n_1 + n_2$. This you can see by simply writing out the equation.
May
27
comment Group of distances
Closed under composition, you mean?
May
27
comment Group of distances
The links in this post give a couple of different proofs that may be useful.
May
27
comment Group of distances
The first one follows from homogeneity and translation invariance, $$r(f(x),f(0)) = r(\frac{g(x)-g(0)}{2^n},\frac{g(0)-g(0)}{2^n}) = 2^{-n}r(g(x)-g(0),g(0)-g(0)) = 2^{-n}r(g(x),g(0)).$$ That $f$ is surjective is the content of the linked answer
May
27
answered Group of distances
May
27
comment Group of distances
Are you saying that $g$ satisfies the mentioned property for some $n$?