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18h
comment Are these two compositions of two functions differentiable?
It is not clear what you are asking.
2d
comment Sufficient condition for $0$ to be in a closed convex hull in a Hilbert space.
@Doug: No, you just need to show that every point of $A$ is contained in the closure of $B$.
2d
awarded  Enlightened
2d
comment Sufficient condition for $0$ to be in a closed convex hull in a Hilbert space.
@Doug: If $0$ is not in the closure, you can find a functional $\phi$ separating the compact set $\{0\}$ from the closure of $C$. That is, there are $\alpha, \beta$ such that $\operatorname{re} \phi(x) \le \alpha < \beta \le \operatorname{re} \phi(0) = 0$ for all $x \in \overline{C}$. That is, $\sigma_C(\phi) < 0$.
Jun
28
awarded  Nice Answer
Jun
28
comment derivative of a function including a vector
You notation is inconsistent, so it is difficult to guess what you are asking.
Jun
28
answered Show that $A^{n}\to0$ if and only if $\|A\|^{n}\to0$
Jun
28
comment Sufficient condition for $0$ to be in a closed convex hull in a Hilbert space.
@Doug: let $\sigma_C(h) = \sup_{c \in C} \operatorname{re} \langle h, c \rangle$.
Jun
28
answered What is the remainder when $6\times7^{32} + 7\times9^{45}$ is divided by $4$?
Jun
28
comment Simple Expected Value Of Continuous Variable Question
One can show it using Fubini Tonelli. Here is a similar question: math.stackexchange.com/q/1329112/27978.
Jun
28
comment Is $K =\{ S: \exists \text{ positive diagonal} D, D^TSD \;\text{diagonally dominant}\}$ convex?
$K$ is trivially convex because $0 \in K_0$ and $0^T S 0 = 0 \in K_0$ for all $S$. Presumably you have some other constraints in mind?
Jun
27
comment Map 1 to 1 and 0 to -1.
$x \mapsto -1+2x$.
Jun
27
comment Regarding linear dependence and independence for finite sequences of vectors
The authors were smoking something at the time.
Jun
27
comment Is u • v equal to |u • v|?
It might help to use $\|u\|$ rather than $|u|$ for norms, and save $|\cdot|$ for absolute values...
Jun
26
comment Prove that $I_n=\int_0^{\frac{\pi}{4}} \tan^{2n}(t)\, dt$ is convergent to $0$
Please clarify the question.
Jun
26
revised what is the geometry behind the matrix multiplication?
added 187 characters in body
Jun
26
comment what is the geometry behind the matrix multiplication?
@gloom: On reflection I'm not so sure that the above a good approach. I was thinking of matrix multiplication as in multiplying a single vector as opposed to another matrix. Obviously matrix multiplication can be interpreted as multiplying the columns, but I don't think this will clarify anything for 11th graders.
Jun
25
comment $n! \le n^n$, $\forall$ $n \ge 1$.
Try induction, dividing, anything.
Jun
24
revised Prove $P(\bigcup_{i=1}^n E_i) \geq \max_i P(E_i)$ for $n≥1$
added 375 characters in body
Jun
24
answered Prove $P(\bigcup_{i=1}^n E_i) \geq \max_i P(E_i)$ for $n≥1$