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Jan
27
accepted Example of continuous function over $\mathbb R^n$
Jan
27
revised Example of continuous function over $\mathbb R^n$
added 1 character in body
Jan
26
comment Example of continuous function over $\mathbb R^n$
$\epsilon-\delta-$ proof is used for real-valued functions so I think it couldn't applied for my case.
Jan
26
asked Example of continuous function over $\mathbb R^n$
Jan
26
comment Intersection of “positive” open half-spaces
Thank you @copper.hat. I got it.
Jan
26
accepted Intersection of “positive” open half-spaces
Jan
26
comment Intersection of “positive” open half-spaces
Dear @copper.hat. Can you give me the explanation why the equation $[x_1^T \ldots x_n^T]^T a = [1 \ldots 1]^T$ always has solution?. This would be a very nice solution for me.
Jan
26
comment Intersection of “positive” open half-spaces
Thank you @copper.hat. If we assume that $V=\mathbb R^n$ then your terminologies "$(\cdot, \cdot)$ is the inner product on $V$" and "the latter inner product is the standard inner product on $\mathbb{R}^n$" are identical isn't it?
Jan
26
comment Intersection of “positive” open half-spaces
Thank you @copper.hat. Since your notation had a bit different to mine so I would like to address some questions. I suppose so $V=\mathbb R^n.$ What did your notations $y_k,x_k,e_k$ mean? And I don't really get the point of "Define an inner product on $\mathbb R^2$ by $\langle a,b \rangle_V = (\phi(a),\phi(b) )$". Why $\mathbb R^2$ here? Thank you.
Jan
25
asked Intersection of “positive” open half-spaces
Sep
14
asked An algebra question for vectors in R^2
Sep
5
comment recurrence relation of a finite sequence
If I assume the characteristic equation $x^2-ax-b=0$ has two different roots $x_1,x_2$ can I deduce that $v_{k}=Ax_1^k+Bx_2^k, k=1,2,\ldots,n$?
Sep
5
comment recurrence relation of a finite sequence
Your answer is very easy to follow, @amcalde thank you. Btw, what is the range of $k$ in your formula of $v_k$? I wonder $k=1,2,\ldots,n$ or $k \ge 1$?
Sep
5
comment recurrence relation of a finite sequence
Thank you @Mark Bennet. Nice explanation. That means even the recurrence relation is true for finite numbers $k$ we can still have the general formula for $v_k$, isn't it?
Sep
4
comment recurrence relation of a finite sequence
I often work with infinite sequences so that if the recurrence relation is satisfied for $k \ge 1$ then we can deduce the general formula for $v_k, k \ge 1$. What happens if the relation is just satisfied for finite numbers $k$ for instance here $k=1,2,\ldots,n-2$?
Sep
4
asked recurrence relation of a finite sequence
Jul
2
awarded  Curious
May
18
comment Waiting time in a bus stop
Thank you for your detailed solution solving the problem over uniformly distributed version.
May
18
accepted Waiting time in a bus stop
May
18
comment Waiting time in a bus stop
@AndréNicolas. Thank you for your answer solving both versions. Actually, I mean that the first bus of day comes in at 7am and after any 15 minutes there is other comimg. In the case my attemping correction is still not clear. Can we do a "trick" that whenever problems refer an assumption like "7 and 7:30", the problems is automatically considered over uniform distribution?