Lx=d: SundayResearch

(The English translation is below the German text.) Normalerweise verwende ich platex um Japanisch zu schreiben. Damit kann ich einen japanischen und einen englischen Text zusammen in einem LaTeX Dokument verfassen. Aber als ich einen deutschen Text unter Verwendung des Babel Pakets hinzugef"ugt habe, wurde die folgende Warnung angezeigt: Package babel Warning: No hyphenation patterns were loaded for the language `ngerman'. Ich habe im Internet danach gesucht, ob jemand diese drei Sprachen gleichzeitig verwendet hat, aber ich konnte nichts dazu finden. (In der Vergangenheit gab es ein "ahnliches Problem auf das sich die Warnung bezogen hat. Aber dieses wurde schon gel"ost.) Es scheint, als ob einige Dateien mit initex erneut kompiliert werden m"ussen. Das platex Paket von Ubuntu machte dies jedoch nicht. Ich vertraue immer auf die Worttrennung von LaTeX. Aber gestern hat meine Tandempartnerin bemerkt, dass der Bindestrich bei ,,in meiner Heimatstadt'' a...

It is election time in Germany. I can find quite a lot of notice boards. I was surprised that one political party's motto is "More tax to everyone" This party got a lot of votes at Saarland recently. Actually, they did not directory say it, but they have two slogans: 1. Reichtum besteueren (Tax the rich: Front side) 2. Reichtum fuer alle (Rich for everyone: Back side) "More tax to rich people" and "Everyone should be rich", therefore, "More tax to everyone." Am I missing something? My friend L. told me this. Front side Back side

Finally I would like to talk about cool matrices. Let's think about a three dimensional vector [x1 x2 x3]' = x1 [x2] x3. (Here ' means transpose.) The vector of difference of each term is [(x1 - 0) (x2 - x1) (x3 - x1)]'. Let's think about a matrix A that makes this difference in the right hand side. I will tell you why we think such a matrix. A is [ 1 0 0 -1 1 0 0 -1 1]. Let's check it out. [ 1 0 0 [x1 [ x1 - 0 -1 1 0 x2 = x2 - x1 0 -1 1] x3] x3 - x2 ] For instance, use [x1 x2 x3]' = [1 4 9]', [ 1 0 0 [1 [ 1 -1 1 0 4 = 3 0 -1 1] 9] 5 ]. The right hand side is the difference of each term. By the way, this matrix has its inverse matrix B, [1 0 0 1 1 0 1 1 1]. Let's compute A B, [ 1 0 0 [1 0 0 [ 1 0 0 [1 0 0 -1 1 0 1 1 0 = (-1+1) 1 0 = 0 1 0 0 -1 1] 1 1 1] (-1+1) (-1+1) 1] 0 0 1]. Therefore, A^{-1} = B. Please be patience a bit more...

There are so many applications of this linear operation. For example, one day's total sales of a supermarket can be computed in the same way: price of item 1 * number of sold of item 1 + price of item 2 * number of sold of item 2 + ... Again, price of item 1 * price of item 2 has no meaning here and therefore, we should not do that. Matrix is useful when we want to perform this kind of operation. Of course we can use matrix (so many) different ways, even so this is still useful. Until here, I hope this is understandable for a junior high school student. But, I realize I could not reach the entitled theme, a cool matrix, in this pace. Then, I will skip several topics, like, what is the relationship between a linear operation and a matrix. I am going to talk about a cool matrix in the next article. The audience would be a bit limited. I assume you know what is matrix or vector and how to write down this language, also can speak a bit. So I assume the audience is a high school stude...