Reputation
71,380
Next tag badge:
97/100 score
63/20 answers
Badges
3 31 95
Newest
 Nice Answer
Impact
~1.3m people reached

Nov
15
answered Show that $x \mapsto \left( x^{\top} \sigma x , -\mu^{\top}x \right)^{\top}$ transforms a given set into a convex set.
Nov
15
comment Show that $x \mapsto \left( x^{\top} \sigma x , -\mu^{\top}x \right)^{\top}$ transforms a given set into a convex set.
This seems unlikely to be convex without additional constraints (or fewer constraints!). Let me see if I can find a counterexample.
Nov
15
comment What is an example for the mean-value theorem to fail to hold for differentiable functions $\mathbb{R}^{n} \to \mathbb{R}^{m}$ if $m \geq 2$?
The first and second component of $f'(c)$.
Nov
15
answered What is an example for the mean-value theorem to fail to hold for differentiable functions $\mathbb{R}^{n} \to \mathbb{R}^{m}$ if $m \geq 2$?
Nov
15
comment Find a matrix X∈V such that U∩W=span{X}
It might be easier to work with $U^\bot, W^\bot$.
Nov
15
comment $\{X_n\}$ are iid random variables with symmetric distribution
Thanks Joe. I think two things are throwing me, one is notation, and the other (bigger one) is that I am not getting the general idea of the proof. I will try again tomorrow.
Nov
15
comment $\{X_n\}$ are iid random variables with symmetric distribution
I am having difficulty following your proof. For example, the 3rd paragraph. You have if some condition then $P(E_{n+1}) = ...$, but the probability of the event $E_{n+1}$ cannot depend on the condition? I am missing something...
Nov
14
comment $AB=BA$ with same eigenvector matrix
For example, if $S_1$ works, then so does $-S_1$. Where exactly in Strang did you read that?
Nov
14
comment Unitary transformation and Orthogonal transformation.
Try using Google with the search string "unitary orthogonal difference".
Nov
14
answered Prove $\sup(f^2(x))\le(\sup(f(x))^2$
Nov
14
comment Showing independence of $\{1,\cos x, \sin x, \ldots, \cos nx, \sin nx\,,\ldots\}$
Arbitrary non-zero integers. By integrating $f$ multiplied by the appropriate function over $[0,2 \pi]$ you can 'pick out' the relevant multiplier.
Nov
14
revised Showing independence of $\{1,\cos x, \sin x, \ldots, \cos nx, \sin nx\,,\ldots\}$
added 2 characters in body
Nov
14
comment Showing independence of $\{1,\cos x, \sin x, \ldots, \cos nx, \sin nx\,,\ldots\}$
@Jon: You can use any tricks you want.
Nov
14
answered Showing independence of $\{1,\cos x, \sin x, \ldots, \cos nx, \sin nx\,,\ldots\}$
Nov
14
comment Showing independence of $\{1,\cos x, \sin x, \ldots, \cos nx, \sin nx\,,\ldots\}$
Orthogonal makes no sense unless you have some added structure. You can add the structure, of course...
Nov
14
comment Showing independence of $\{1,\cos x, \sin x, \ldots, \cos nx, \sin nx\,,\ldots\}$
Its the same, just pick a finite number of terms.
Nov
14
comment Calculating the nested area
You need go give a little more information.
Nov
14
answered Bound remainder of Taylor series with Lipschitz property of derivative
Nov
14
revised Prove $\|\cdot\|_s$ is a norm, and find $m,M>0$ such that $m\|x\|_\infty\leq \|x\|_s\leq M\|x\|_\infty$
added 110 characters in body
Nov
14
comment Prove $\|\cdot\|_s$ is a norm, and find $m,M>0$ such that $m\|x\|_\infty\leq \|x\|_s\leq M\|x\|_\infty$
I added an approach below which moves the cases to showing the unit ball is convex.