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Jul
26
comment If $x_n \to a$ and $x'_n \to a$, then $\{x_1, x'_1, x_2, x'_2, …\} \to a$
Multiplying the indices by any number $\ge 2$ will work. Remember the sequence is $(y_1,y_2,y_3,y_4,...) = (x_1,x_1', x_2,x_2',...)$. The corresponding indices are $(1,2,3,4,...)$ and $(1,1,2,2,...).
Jul
26
comment What is the remainder when $6\times7^{32} + 7\times9^{45}$ is divided by $4$?
Why the downvote?
Jul
26
comment If $x_n \to a$ and $x'_n \to a$, then $\{x_1, x'_1, x_2, x'_2, …\} \to a$
@morphic: The $N,N'$ come from considerations on $x_n,x_n'$, to 'convert' the $N,N'$ for use with $y_n$ you need to multiply by 2.
Jul
15
comment invertible matrices connected or not
It is straightforward to define a $\log$ for invertible matrices.
Jul
15
comment Taylor series for $\sqrt{x}$?
@bclc: The Maclaurin series...
Jul
14
comment Given $|f'(x)|\leq r<1$ show that $f(x)=x$ is unique solution
Why the downvote?
Jul
14
comment Taylor series for $\sqrt{x}$?
@bclc: No, it doesn't exist for $x_0=0$, it does exist for $x_0>0$.
Jul
9
comment Using Least Squares to calculate a matrix in an equation.
What norm? ${}{}{}$
Jul
4
comment Difference between parentheses and angle brackets in vector notation
@Zaz: My comment was meant in a light hearted way. Some folks use $]0,1[$ to indicate an open interval to avoid confusion with other notations (inner product, pairs, etc.). However, in practice there is rarely a confusion.
Jul
1
comment Are these two compositions of two functions differentiable?
It is not clear what you are asking.
Jun
29
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 $B$.
Jun
29
awarded  Enlightened
Jun
29
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?