Recent content by Impo

Thanks for the help Opalg!1. Let's check (y_n)_n \in H, that is \sum_{n=1}^{\infty} y_n < \infty. We have \sum_{n=1}^{\infty} y_n = \sum_{n=1}^{\infty} \lim_{m \to \infty} x_n^{(m)} = \lim_{m \to \infty} \sum_{n=1}^{\infty} x_n^{(m)} < \infty. The last inequality follows from the fact that...

Hi, Let H = \{(x_n)_n \subseteq \mathbb{R} | \sum_{n=1}^{\infty} x_n < \infty \} and for $(x_n)_n \in H$ define $$\|(x_n)_n\|_H = \sup_{n} \left|\sum_{k=0}^{n} x_k \right|$$ Prove that $H$ is complete. Is $H$ a Hilbert space? What is the best way to prove $H$ is complete? To prove it's a...

AB = \left( \begin{array}{ccc} 2 & 0 & 0 \\ 0 & -3 & 0 \\ 0& 0&6 \end{array} \right) $\Leftrightarrow A = \left( \begin{array}{ccc} 2 & 0 & 0 \\ 0 & -3 & 0 \\ 0& 0&6 \end{array} \right)B^{-1}$ $\Leftrightarrow A = \mbox{I}_3 \left( \begin{array}{ccc} 2 & 0 & 0 \\ 0 & -3 & 0 \\ 0& 0&6...

If \{e_1,e_2,e_3\} is the canonical basis for \mathbb{R}^3 then the only thing I can say is A(Be_1)=(2,0,0)^{T} and so on But I don't see how this helps me ... I think I don't quite understand the purpose of this.

I have no idea, I don't know anything about $A$. But I thought that semi-axes of the ellips were the vectors Ax?

Honestly, I don't understand what you mean ...

Hi Suppose that A \in \mathbb{R}^{3 \times 3} who maps the unit sphere in \mathbb{R}^3 to an ellips with the following semi-axes; x = \left(-\frac{1}{\sqrt{2}}, -\frac{1}{\sqrt{2}},0\right)^{T} \mapsto Ax = (2,0,0)^{T} x=\left(-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}},0\right)^{T} \mapsto Ax =...

Thanks for the answer! I found a method now to solve it (it's called the SA algorithm), I only have some troubles with programming in matlab. First I need to write a code for the encryption of playfair, the problem is I have no idea how to implement a code for the 5x5 matrix with the key word in...

Hi all, I hope my post is in the right section. I need some help with decoding a Playfair code. I only have the ciphertext which is 22 lines long. What's the best way to do this? I red that I have to do some frequency analysis of the English bigrams which I did. There's one combination which...