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Feb
23
comment Can I get the upper bound of the $L_2$ norm of a symmetric matrix?
2-norm is the largest singular value.
Feb
23
comment Proving that an $m \times n$ matrix has rank 1
Please post your exercise.
Feb
10
comment If $(a_n)$ is a decreasing sequence of strictly positive numbers and if $\sum{a_n}$ is convergent, show that $\lim{na_n}=0$
How did you show $\lim_{n\to\infty}na_n$ exist?
Jan
29
comment Why is a vector function not smooth if $r'=0$
It's like you walk, stop, and (probably turn and) walk again. There will a singularity in the route.
Jan
17
comment Laplace, Legendre, Fourier, Hankel, Mellin, Hilbert, Borel, Z…: unified treatment of transforms?
@Startwearingpurple Can separable Hilbert space have uncountable orthonormal basis?
Jan
12
comment When do matrices have positive eigenvectors?
What's a positive eigenvector?
Jan
11
comment Prove that $(a-b)^n\mid (a^n-b^n) \iff n=1$ under given conditions
Why is it the hardest?
Jan
11
comment Find the sum $\sum_{k=2}^n \frac{n!}{(n-k)!(k-2)!}.$
$LHS=\frac{n!}{(n-2)!}\sum_{k=0}^{n-2}\frac{(n-2)!}{(n-2-k)!k!}=n(n-1)2^{n-2}$
Jan
7
comment Show that $rank(A) \ngeq \frac{[tr(A)]^2 }{tr(A^2)}$
Does >/= mean <?
Oct
2
comment Every convex function is continuous
@RFZ any $t<u_1<b$ and $a<u_2<s$ are OK.
Oct
2
comment Every convex function is continuous
There is $u_1$ such that $f(t)-f(s)\le\frac{f(u_1)-f(t)}{u_1-t}(t-s)=L_1(t-s)$. Similarly there is $u_2$ such that $f(t)-f(s)\ge\frac{f(t)-f(u_2)}{t-u_2}(t-s)=L_2(t-s)$. So $|f(t)-f(s)|\le L|t-s|$ for some $L$.
Jul
15
comment What are the general steps to turn a PDE into a dynamical system $\dot x(t)= Ax(t) + Bu(t)$
Check textbooks on control theory. The wiki page may also help: en.wikipedia.org/wiki/State-space_representation
Apr
10
comment How many distinct elements are there in $C=\{zw\mid z∈A$,$w∈B\}, z^{24}=1$ and $w^{54}=1$.
But this is anyway an algebra problem.
Apr
6
comment Why are additional constraint and penalty term equivalent in ridge regression?
Can you briefly summarize the paper (since the journal version has some pages)?
Apr
6
comment Why are additional constraint and penalty term equivalent in ridge regression?
If $\alpha=0$, does it mean the corresponding $c$ can be any non-negative number, according to the second KKT condition?
Jan
27
comment Does Euclidean division not work for general polynomials?
ED implies PID. But only polynomials of one variable can form a PID. So no.
Nov
16
comment How to find $x$ such that $\tan5x=\tan x$ and $\sin5x=\sin x$?
You are welcome :)
Aug
12
comment What is the oldest open problem in geometry?
I would like to see an animation for a periodic orbit in an obtuse triangle.
Jul
11
comment Limit of the integral: $\int_0^{\pi/2}\beta^\alpha\exp\left(-\beta\cos(\theta)\right)d\theta$
Shouldn't it be $\lim_{\beta\to+\infty}J_0(\beta)=0$? Illustration.
Jul
4
comment 'Obvious' theorems that are actually false
You may be interested in these books: Counterexamples in Analysis, Counterexamples in Topology, and Counterexamples in Probability.