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Jul
14
comment Basic question about multilinear forms
Shouldn't there be a $\oplus$ instead of $\otimes$ on the right hand side?
Jul
14
comment Notation - “' sign” in summation
It can appear otherwise, allthough it is not very readable, a variable can appear both bounded and free in an expression.
Jul
7
comment Group action of $GL(2, F)$ on the projective line $P(F)$
You are right in assuming that iff $c=0$, we define $s_\alpha(\infty) = \infty$. The author just forgot to mention it, I think.
Jul
6
comment Expressing a function in terms of compositions of three functions.
Are there any restrictions on the form of $f,g,h$? Otherwise the task does not make much sense, as one can take $h = F$, $g(x) = f(x) = x$ for example ...
Jul
6
comment If a sequence of self-adjoint linear operators is convergent, show that its limit is self-adjoint.
Convergent in what sense?
Jul
6
comment Efficient Test For Commuting Matrices
... and $n^3$ can be approved: Using Strassen multiplication, we have $O(n^{2.8\cdots})$
Jul
6
comment How to solve this combinations with repetitions problem using generating functions?
Added somehing @idandi
Jul
6
comment How to solve this combinations with repetitions problem using generating functions?
Not the explanations! The lines starting with '%...' in the source!
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