The orthogonal group is the group of all invertible matrices where the inverse is equal to the transpose by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Let's show that this definition is equivalent to the orthogonal group is the group of all matrices that preserve the dot product.
Note that:and for that to be true for all possible and then we must have:i.e. the matrix inverse is equal to the transpose.
These matricese are called the orthogonal matrices.
TODO is there any more intuitive way to think about this?
Trapped ion people acknowledge that they can't put a million qubits in on chip (TODO why) so they are already thinking of ways to entangle separate chips. Thinking is maybe the key word here. One of the propoesd approaches inolves optical links. Universal Quantum for example explicitly rejects that idea in favor of electric field link modularity.
FeathersJS entry for gothinkster/realworld.
MongoDB-based.
So once you install MongoDB, run with:
MONGODB_FEATHERS_REALWORLD=mongodb://localhost:27017/mydb npm startGot it working on Ubuntu 20.10 with both React and Vue.js front-ends at github.com/randyscotsmithey/feathers-realworld-example-app/commit/8bc3a09242285de624c75bb8345630df499a7d07 as mentioned at github.com/randyscotsmithey/feathers-realworld-example-app/issues/2 except for bad error reporting on UI.
Tests can be run with:but there were 10 failures and 55 passes: github.com/randyscotsmithey/feathers-realworld-example-app/issues/3
MONGODB_FEATHERS_REALWORLD=mongodb://localhost:27017/mydb npm run testCombination of electromagnetism and general relativity. Unlike combining quantum mechanics and general relativity, this combination was easier.
TODO any experiments of interest at all?
Section type:
sh_type == SHT_SYMTAB.A good high level tool to disassemble that section is:which gives:
nm hello_world.o0000000000000000 T _start
0000000000000000 d hello_world
000000000000000d a hello_world_lenThis is however a high level view that omits some types of symbols and in which the symbol types . A more detailed disassembly can be obtained with:which gives:
readelf -s hello_world.oSymbol table '.symtab' contains 7 entries:
Num: Value Size Type Bind Vis Ndx Name
0: 0000000000000000 0 NOTYPE LOCAL DEFAULT UND
1: 0000000000000000 0 FILE LOCAL DEFAULT ABS hello_world.asm
2: 0000000000000000 0 SECTION LOCAL DEFAULT 1
3: 0000000000000000 0 SECTION LOCAL DEFAULT 2
4: 0000000000000000 0 NOTYPE LOCAL DEFAULT 1 hello_world
5: 000000000000000d 0 NOTYPE LOCAL DEFAULT ABS hello_world_len
6: 0000000000000000 0 NOTYPE GLOBAL DEFAULT 2 _startThe binary format of the table is documented at www.sco.com/developers/gabi/2003-12-17/ch4.symtab.html
The data is:which gives:
readelf -x .symtab hello_world.oHex dump of section '.symtab':
0x00000000 00000000 00000000 00000000 00000000 ................
0x00000010 00000000 00000000 01000000 0400f1ff ................
0x00000020 00000000 00000000 00000000 00000000 ................
0x00000030 00000000 03000100 00000000 00000000 ................
0x00000040 00000000 00000000 00000000 03000200 ................
0x00000050 00000000 00000000 00000000 00000000 ................
0x00000060 11000000 00000100 00000000 00000000 ................
0x00000070 00000000 00000000 1d000000 0000f1ff ................
0x00000080 0d000000 00000000 00000000 00000000 ................
0x00000090 2d000000 10000200 00000000 00000000 -...............
0x000000a0 00000000 00000000 ........The entries are of type:
typedef struct {
Elf64_Word st_name;
unsigned char st_info;
unsigned char st_other;
Elf64_Half st_shndx;
Elf64_Addr st_value;
Elf64_Xword st_size;
} Elf64_Sym;Ciro Santilli finds it interesting that radioactive decay basically kickstarted the domain of nuclear physics by essentially providing a natural particle accelerator from a chunk of radioactive element.
The discovery process was particularly interesting, including Henri Becquerel's luck while observing phosphorescence, and Marie Curie's observation that the uranium ore were more radioactive than pure uranium, and must therefore contain other even more radioactive substances, which lead to the discovery of polonium (half-life 138 days) and radium (half-life 1600 years).
Does not appear to refer to any one specific phylogenetic level, it usually refers to either:
- Saccharomyces cerevisiae, the model eukaryote unicellular organism
- two phila of the fungus kingdom
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact