28,886 reputation
1938
bio website jungenschaft-hohenstaufen.de
location Berlin, Germany
age 33
visits member for 2 years, 7 months
seen Mar 31 at 9:56

Jan
24
comment Is any subset of the open ordinal space $[0,\Omega)$ $G_\delta$?
No. See dantopology.wordpress.com/2009/10/11/… ... property C.
Jan
24
comment if $A+B+C+D=\pi$, what is $\min(\cos{A}+\cos{B}+\cos{C}+\cos{D})$
@nanchangjian And? Up to multiplies of $2\pi$, in your example $A=B=C$.
Jan
24
comment are the regular topology on $\mathbb R$ and the product topology on $\omega^\omega$ equivalent?
In what sense you want to compare $\omega^\omega$ with $\mathbb R$. If you are looking at the embedding $\omega^\omega \cong \mathbb R \setminus \mathbb Q \subseteq \mathbb R$ via continued fractions, then the answer is: Yes, $\omega^\omega$ is homeomorphic with the irrationals.
Jan
22
comment Is $f$ uniformly continuous
If $f$ were uniformly continuous, there would be a uniformly continuous extension $F\colon [0,1] \to \mathbb R$.
Jan
22
comment A Property of Lyapunov Index
@Vincent $\log 2/t \to 0$, so $\lambda(2f) = \lambda(f)$.
Jan
17
comment Multiplication operator $M_\phi$
@nika Consider $M_\phi(1)$. Note, that $1 \in L^2(\mu)$, as $(X, \Omega, \mu)$ is finite.
Jan
15
comment derivate of a Trace operator
The definition of derivative I used is the following: $A$ is differentiable in $U$ iff there is a linear $A'(U) \colon \Mat_n(\R) \to \R$ such that $$ A(U+H) = A(U) + A'(U)H + o(\norm H), \quad H \to 0 $$ Then $A'(U)$ is called the derivative of $A$ in $U$. What definition do you know?
Jan
15
comment derivate of a Trace operator
And $U$ and $W$ are quadratic of the same size, right?
Jan
10
comment Integral and differentiable function
As the right hand side does not depend on $T$, $K$ is a constant function. I think that is not what you wanted to write, are $\beta, \delta$ $T$-dependent?
Jan
10
comment If $AB=-I_n$, then prove that $det(I_n+BA)=2^n$
We have $$ I + BA = B(B^{-1} + A) = B(I + AB)B^{-1},$$ that is $I + BA = 0$ under the given hypotheses.
Jan
9
comment A question on Cauchy sequence in topological abelian group
@MartinBrandenburg Thx. Done.
Jan
8
comment Prove that the set of one-to-one function $f: S\to S$ is a group with composition as group operation.
The one-to-one functions do not form a group. The one-to-one and onto functions do.
Jan
3
comment Product of positive matrices
$xx^T \ne x^Tx = \|x\|^2$.
Dec
18
comment Resolvent properties
What is $q_i$? $Q$'s $i$th row?
Dec
15
comment If $f(x)$ is differentiable on $(a,b)$, is $f(x)$ continuous on $[a,b]$?
And even if $f$ is defined on $[a,b]$, $f$ needn't be continuous there, e. g. $$ x \mapsto \begin{cases} \sin x^{-1} & x > 0\\ 0 & x = 0 \end{cases} $$
Dec
15
comment Is Wolfram Alpha wrong with a simple derivative?
Just add a * to tell wolfram you want multiplication, not application ... and everything works as expected: wolframalpha.com/input/?i=d[%28x^2w*%28y-z%29t%29%2F%2818l%29%2Cw]
Dec
15
comment How do I normalize these vectors? Gram-Schmidt simple question
@OriaGruber: No. $\int_{-1}^1 x^2 \,dx = \frac 23$. Hence $\|x\|_2 = \sqrt{\frac 23}$. And in LaTeX, the $\|$ is done by \| (nicer spacing than $||$).
Dec
15
comment How do I normalize these vectors? Gram-Schmidt simple question
If you are given an inner product, as in your space, the corresponding norm is given by $\|f\|_2 = \left<f,f\right>^{1/2}$.
Dec
15
comment How do I normalize these vectors? Gram-Schmidt simple question
The noem of an $f\in \mathbb R[X]_{\le 3}$ is given by $\|f\|_2 = \left(\int_{-1}^1 f(x)^2\, dx\right)^{1/2}$. Just compute the norms and divide by them ...
Dec
13
comment Improper Multivariable Integrals
The second integral converges at infty (in the Lebesgue sense) if the exponent or $r$ is less then $-1$, as the sine is bounded ...