Recent content by nacho-man

$\chi$ the relation that I put was the one we are given to derive. So I guess the assumption is $\theta < \frac{\pi}{2}$, which is also consistent with the diagram given. I.e We are told the recurrence relation is :$x_{n+1} = x_n - y_n \tan(\theta_{n+1})$ and $y_{n+1} = y_n + x_n...

Still helpful as ever chi sigma! Thank you my friend. Could I just clarify which formula you used to get the recursive relationship? can it be found on this page anywhere?: Trigonometric Identities I am thinking it is this one: $\cos(α + β) = \cos(α)\cos(β) – \sin(α)\sin(β) $Although, the...

Given the image: http://i.stack.imgur.com/EJ3ax.jpgand that $x_0 = 1, y_0=0$ and $\text{angles} \space θ_i , i = 1, 2, 3, · · ·$ can be arbitrarily picked. How can I derive a recurrence relationship for $x_{n+1}$ and $x_n$? I actually know what the relationship is, however, don't know how to...

Yes! definitely. I will post the solution some time next week, when my work has been assessed (don't want to post a solution with errors and mislead someone :( )

I have solved this problem now. Thanks :)

It has been eons since I've done any trigonometry, but I just can't prove how this following relationship holds for $n = 4, 8, 16, 32, \dots$ The relation is: $$ 2 \biggl( \! \frac{A_{2n}}{n} \! \biggr)^2 = \, 1 - \Biggl( \sqrt{1 - \frac{2A_n^{\phantom{X}}}{n}} \, \Biggr)^{\!2} $$ I've subbed...

this was a suspicion of mine - thank you!

anyone? :( If I wasn't clear, $x^* = (x_1,x_2)$

Assuming $x_1, x_2 \geq 0, \lambda \neq 0, w_1,w_2 > 0$ We have the equalities: $$w_1 - \lambda x_2 = 0 ... (1)$$ $$w_2 - \lambda x_1 = 0 ... (2)$$ $$\bar y - x_1x_2= 0 ... (3)$$ My solutions say that $\lambda^* = \sqrt\frac{w_1w_2}{\bar y}$ Which I was able to solve myself. The other...

Sorry I could have worded my previous post a lot better, let me re-iterate what I was trying to say When I say "take" I meant just select some $\{x_n\}_n$ and $\{y_n\}_n$ in $V(A)$ and add them together. In regards to not properly introducing the $x$ and $y$ terms, I was just going off the...

So assume $A$ is a subspace. we take $\{x_n\}_n + \{y_n\}_n \in V(A)$ $$\because \{x_n\}_n + \{y_n\}_n = x + y = a \in A$$ $$\therefore \{x_n\}_n + \{y_n\}_n \in V(A)$$ (not sure if I have sufficiently justified this) Hence the set is closed under addition. Then, $$\forall \lambda \in...

thanks for your reply, I see exactly what you mean about where my proof didn't make sense. So how exactly would I show that $V(A)$ is a subspace? I don't see how working with the assumption that $A$ is a subspace is of any benefit to me? If $A$ is a subspace, its closed under addition and...

Hi everyone, would really appreciate if someone could help me with the attached question (its the one in the red box). My start: Assume $A$ is a subspace. We need to show that $V(A):= \{ \{x_n\}_n \in V_0 : \lim_{{n}\to{\infty}}x_n \in A \} $ By definition, a subspace is closed under...

Thank Ackbach, I'll be sure to check these titles out!

Hi everyone, I will be taking a summer course on Optimisation - AMSI Summer School and was wondering if you could recommend any books. The course outline is: Week 1: Introduction to Optimization problems: classification and examples. Elements of convex analysis: convex sets and convex...