, 7 min read
Die Eigenwerte einer Matrix hängen stetig von den Komponenten der Matrix ab. Dies soll hier bewiesen werden. Man kann sogar noch weitere Abhängigkeitssätze beweisen, jedoch werden die Begründungen dann länger, siehe das Buch von Gohberg/Lancaster/Rodman (1982), Autoren sind Gohberg, Izrael'…
, 6 min read
1. Die Spur (engl./franz.: trace) einer Matrix $A\in\mathbb{C}^{n\times n}$ ist definiert zu $\def\tr{\mathop{\rm tr}}\tr A=a_{11}+\cdots+a_{nn}$, somit die Summe der Hauptdiagonalelemente. Durch elementare Rechnung zeigt man $\tr AB=\tr BA$, für zwei beliebige Matrizen $A\in\mathbb{C}^{n\times…
, 8 min read
Hermitesche Matrizen $(\def\adj#1{#1^*}\adj A=A)$, unitäre Matrizen $(\adj A=A^{-1})$ und normale Matrizen $(\adj AA=A\adj A)$ lassen sich unitär diagonalisieren. Dies ist das zentrale Ergebnis dieses Abschnittes. Während die Jordansche Normalform für jede komplexe Matrix…
, 5 min read
1. Definition: Ein Polynom $f(x_1,\ldots,x_n)$ in den Unbestimmten $x_1,\ldots,x_n$ heißt symmetrisch, falls das Polynom invariant bleibt unter jeder beliebigen zyklischen Vertauschung der Unbestimmten. 2. Beispiel: $f(x_1,x_2)=x_1^2+x_2^2$ oder $f(x_1,x_2)=x_1^3+x_2^3$ sind symmetrische…
, 21 min read
1. Das äußere Produkt 2. Definition einer Determinante 3. Eigenschaften einer Determinante 4. Der Laplacesche Entwicklungssatz 5. Weitere Folgerungen aus dem Satz von Cauchy/Binet 1. Das äußere Produkt Es gibt eine Fülle von Möglichkeiten Determinanten einzuführen. Ein Weg ist, über das…
, 1 min read
As of today the following open-source projects have the below lines of code (LOC). Name LOC in million Linux kernel 34.987 Chrome 30.992 PHP 1.814 Apache HTTP Server 1.659 WordPress 1.157 Slurm 0.844 Git 0.580 X server 0.511 bash 0.249 Zola 0.022 Simplified Saaze 0.002
, 7 min read
Matrixpolynome (oder gelegentlich auch $\lambda$-Matrizen genannt) sind Polynome, bei denen die Koeffizienten Matrizen sind, quadratisch oder rechteckig, dies ist vorerst gleichgültig. Also $$ L(\lambda) = A_\ell\lambda^\ell + A_{\ell-1}\lambda^{\ell-1} + \cdots + A_1\lambda + A_0,…
, 2 min read
I am now a member of the 250KB club. See "Proud member": eklausmeier.goip.de Proud member of the exclusive 250KB Club! Added: 2024-01-19 | Last updated: 2024-01-19 eklausmeier.goip.de is a member of the exclusive 250KB Club. The page weighs only 78kb and has a content-to-bloat ratio of…
, 3 min read
In the previous post Example Theme for Simplified Saaze: Lemire I demonstrated the transition from a website using WordPress to Simplified Saaze. This very blog also uses Simplified Saaze. This post shows how much better performance-wise this transition was. The comparison is therefore…
, 1 min read
Today, 08-Jan-2024, starting at 18:49 (CET), internet provided by Vodafone was unavailable. I called the hotline of Vodafone and they confirmed that they had a major outage in my region. This means: my homepage, i.e., this blog, is unavailable. In 2022 the internet router was defective. This time…
, 6 min read
Cloud-Computing ist in aller Munde. Man hört: Cloud ist modern. Cloud ist grün. Cloud spare Kosten. Cloud ist verkaufsfördernd. Jedoch, die Euphorie bekommt Risse. Die vorhergesagten Kostenersparnisse treten nicht ein. Der Aufbau einer Cloud-Infrastruktur benötigt Zeit und erfordert…
, 8 min read
Another theme for Simplified Saaze called "Lemire". You can inspect it here. This theme is modeled after the blog from Daniel Lemire. That blog is powered by WordPress and hosted on SiteGround and performance enhanded by Cloudflare since 2019. Prof. Lemire started blogging in 2004. The…
, 8 min read
1. Problem statement. You have a Bachelor Thesis in LaTeX. This thesis is converted to Markdown. I had written on a similar topic here: Converting Journal Article from LaTeX to Markdown. 2. Solution. I already knew that a Pandoc approach does not work. For the conversion I modified the two Perl…
, 4 min read
Press release High-resolution three-dimensional maps of the Milky Way have previously been limited to the immediate vicinity of the Sun. In a collaboration led by the Max Planck Institute for Astrophysics with researchers from Harvard, the Space Telescope Science Institute, and the University of…
, 2 min read
Android is based on Linux. Unfortunately, the Linux on Android devices is severely restricted, in particular you cannot easily become the root user. Using Termux and the like you can get a little bit of the "usual" Linux feeling on Android devices. In addition to that, each hardware…
, 9 min read
1. Motivation. I am a regular user of vi/vim/neovim. But one thing, though, is a little bit annoying, when using neovim: even on a fast machine starting neovim takes quite a considerable time to start. Though, this is mostly caused by an elaborate initialization file. mle is a text editor written…
, 5 min read
This blog is self-hosted. One could think that this situation is particularly prone to outages. Actually, this hosting is quite stable compared to professional services. This to my own surprise. Today Cloudflare has its snafu-moments: Cloudflare is assessing a loss of power impacting data centres…
, 3 min read
This is in continuation of Nima Badizadegan on Cloud Computing. David Heinemeier Hansson, creator of Ruby on Rails, cofounder of the HEY e-mail service, prolific writer, made a number of noticeable remarks on cloud costs. David Heinemeier Hansson from 37signals.com wrote We stand to save $7m over…
, 8 min read
This blog uses the PHP-based Simplified Saaze software. I measured Simplified Saaze using XHProf: Profiling PHP Programs Profiling PHP Programs #2 Still I am interested whether I missed anything. In multiple talks Rasmus Lerdorf, the creator of PHP, advertises PHPSPY. PHPSPY was written by Adam…
, 5 min read
Pagefind is a JavaScript library, which you add to your static site. By that you then have complete search-functionality. Pagefind has the following advantages over other JavaScript libraries: Easy to install, no JavaScript dependency hell. Easy to add the CSS and the two lines with <script>…