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Jun
26
comment Hilbert space and uncountable cardinal
You should ask this as a seperate question, but the answer is yes. Consider $$ \mathbf K^{(\kappa)} := \left\{ x \colon \kappa \to \mathbf K \biggm| x^{-1}[\mathbf K \setminus \{0\}] \text{ is finite} \right\} $$ this space has $e^i$, $i \in \kappa$ (defined as above) as basis.
Jun
22
comment Graph vertex set with a certain property
@Arthur Doesn't $V_1$ allready have the stated property? Let $v \in V(G)$ be connected to all vertices in $V_1$. Then $v$ is connected to all vertices in $V_0$ (as $V_0 \subseteq V_1$), hence $v \in V_1$.
Jun
18
comment What is the most intuitive explanation for euler's identity?
$-1$ is one unit to the left ($\pi$ radians from the right, i.e. postive direction) of $0$?
Jun
5
comment To show $B^2$ is diagonalizable
You can also use that (multiply $AB = BA^{-1}$ from the left with $A^{-1}$ and from the right with $A$) $BA = A^{-1}B$ and then directly $$ AB^2 = BA^{-1}B = B^2A $$
May
27
comment Sub graph of a graph up to isomorphism?
@user226045: They are. $a \def\lr{\leftrightarrow}\lr a$, $b \lr b$, $c\lr d$, $d\lr c$ is an isomorphism.
May
27
comment Application Farkas Lemma
Right. Thanks, edited-
May
11
comment showing that 2 matrices are not similar
@marco11 You are right.
May
11
comment showing that 2 matrices are not similar
@marco11 We can. But there is now need to, when we start to compare the eigenspaces, we see that the $2$-eigenspace of $A$ is one-dimensional, while the $2$-eigenspace of $B$ is two-dimensional.
May
11
comment Can anyone help me finding recurrence relation in combinatoric?
@kuhaku As we are looking for words of length $n-1$, which are illegitimate ...
May
8
comment Using chain rule to represent second order derivatives
So we have that $r$ depends on $x$ and $t$, right? And $\beta$?
May
7
comment Integral of $e^{2\sin x}$
This integral is not elementary. The antiderivative of $\exp\bigl(2\sin x\bigr)$ cannot be written explicitly in elementary functions.
May
7
comment Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$
The first two groups are isomorphic, just reorder the elements: escarbille.free.fr/group/?g=6_2b&z=0|5|1|3|2|4
May
7
comment abstract algebra , ideal of a ring of matrices .
$\pi$ is onto ... given $r+I \in R/I$, then $\pi(r) = r+I$.
May
7
comment abstract algebra , ideal of a ring of matrices .
Yes, you are right of course, $\pi[J]$ is an ideal ...
May
7
comment Approximating monotonically increasing differential equation
I don't now, I think its just multiplication. I do not like this notation either.
May
6
comment positive linear maps of $c^*$-algebras are bounded
Are you sure that $A^+$ denotes unitization? In this context (and answering questions 1 and 2) it seems to me that $A^+$ denotes the set of positive elements of $A$.
May
6
comment Cancellative Abelian Monoids II
Note that (think of the naturals) for three elements $a,b,c \in M$ we cannot hope that from $abc = dm$, $d$ is the greatest common divisor, instead we want something like $abc = d^2m$.
May
5
comment Meaning of the composition of functions
No, the order of execution in this example is always first $g$, then $f$, the position of the argument changes the natural way for the notation of composition ...
May
5
comment Plotting Non Linear Programming functions
You want to plot the $f_i$ over what domain? As functions depending on what variables? Also citing the error Matlab gives, often helps: I got Functions must take one argument.
May
5
comment Total Variation of Constant Function
Yes. ${}{}{}{}{}$