does D_n always have the form {identity, r, r^2, ... ,r^n; s, sr, sr^2, ..., sr^n}? where r is a rotation between adjacent vertices and s is reflection
We have this system here that if you don't get accepted they put you in reservation slot
so if someone does get accepted but they reject the offer by themselves then the spot will go to someone that is highest ranking in the reservation slot's
we have on a lot of these courses the policy not use calculators in exams etc.. so i usually try to solve the problem as far as i can without any external aid
whenever there are "maths monsters" here, like ted shrifin, balarka sen, eric silva to name a few, they take about things, i start googling them as i am reading, but the things they say i have never heard of them and i have searched the curriculum here, its not in the courses. Meaning i wont be able to talk like that, Ever (sad face)
@Tuki your hessian is wrong i think. Please check.
Mainly interested, the higher level maths I really have studied are linear algebra, some simple differential equations solving methods and multivariable calculus
and that is back in my 2nd year
All other maths are done by self study and learnt from the chat
It appears the hessian of the lagrange function need to be handled more carefully, thus one cannot tell about minimas and maximas via the eigenvalues https://en.wikipedia.org/wiki/Hessian_matrix#Bordered_Hessian
Never encountered that before in my 2nd year course
so getting an indefinite hessian in your workings suggest at least your hessian is of the correct form, now you need to check whether the minors are -ve
Let $S = [0,1) \cup [2,3]$ and $f\colon S \rightarrow \mathbb R$ be such that $f(S)$ is connected . Which of the following are true:
a) $f$ is discontinuous exactly at one point.
b) $f$ is discontinuous exactly at two points.
c) $f$ is discontinuous at infinite many points.
d) $f$ is continou...
I think so... I don't know until today that hessians of lagrange functions need to be handled in a different way. I also tried plotting the function with the lambda value you solved but find no stationary points in wolfram alpha
though the signs of the 3 principle minors I get are +1,-1,+1 thus it should suggest you have find a minimum to the lagrange function
are there functions $f : \Bbb R^2 \to \Bbb R$ for which the statement $\dfrac {\partial \partial f} {\partial x \partial y} = \dfrac {\partial \partial f} {\partial y \partial x}$ is well-defined and is false?
how fast is going to infinity is too fast, cause one can imagine if $x_n$ decays slower (details unknown) than $y_n$ can grow, the product will blow up
I also suspect if $y_n$ diverges to infinty by blowing up, no amount of $x_n$ can force it finite
This is a bit silly question I found on another discussion forum. I know that determinants can be used to compute volumes of parallelepiped. I also know that determinants can be computed by linear combination of its minors. Is there any geometric meaning of minors or some proof/explanation why th...
Consider the following iterations :
$x_0 = z$
Where $z$ is complex.
$x_n = \frac{ x_{n-1}^2 - 1}{n}$
It is well known that for real $z > 3$ the sequence grows double exponentially.
It is known that for $z = 3$ the sequence grows linear ; in fact like $3,4,5,6,7,...$.
In fact When considering...
@BalarkaSen are you at all good with orientability?
I have a statement I seem to lack enough background on. "the characteristic foliation of a surface S is orientable if and only if the normal bundle of S is isomorphic to the quotient bundle $(TM/\xi)\vert_S$."
Let $S = [0,1) \cup [2,3]$ and $f\colon S \rightarrow \mathbb R$ be such that $f(S)$ is connected . Which of the following are true:
a) $f$ is discontinuous exactly at one point.
b) $f$ is discontinuous exactly at two points.
c) $f$ is discontinuous at infinite many points.
d) $f$ is continou...
Consider the following iterations :
$x_0 = z$
Where $z$ is complex.
$x_n = \frac{ x_{n-1}^2 - 1}{n}$
It is well known that for real $z > 3$ the sequence grows double exponentially.
It is known that for $z = 3$ the sequence grows linear ; in fact like $3,4,5,6,7,...$.
In fact When considering...
