Effect of a change of basis on the matrix of a bilinear form Updated 2025-07-11 +Created 1970-01-01
If is the change of basis matrix, then the matrix representation of a bilinear form that looked like:then the matrix in the new basis is:Sylvester's law of inertia then tells us that the number of positive, negative and 0 eigenvalues of both of those matrices is the same.
Proof: the value of a given bilinear form cannot change due to a change of basis, since the bilinear form is just a function, and does not depend on the choice of basis. The only thing that change is the matrix representation of the form. Therefore, we must have:and in the new basis:and so since:
Strangeness Minus Three (BBC Horizon 1964)
Source. Basically shows Richard Feynman 15 minutes on a blackboard explaining the experimental basis of the eightfold way really well, while at the same time hyperactively moving all over. The word symmetry gets tossed a few times.The Einstein summation convention works will with partial derivatives and it is widely used in particle physics.
In particular, the divergence and the Laplacian can be succinctly expressed in this notation:
In order to express partial derivatives, we must use what Ciro Santilli calls the "partial index partial derivative notation", which refers to variables with indices such as , , , , and instead of the usual letters , and .
One important quantum mechanics experiment, which using quantum effects explain the dependency of specific heat capacity on temperature, an effect which is not present in the Dulong-Petit law.
This is the solid-state analogue to the black-body radiation problem. It is also therefore a quantum mechanics-specific phenomenon.
See also: e-learning website.
E-learning websites must keep content free, only charge for certification Updated 2025-07-11 +Created 1970-01-01
Another thing that is fine charging for is dedicated 1-to-1 tutor time. This is something Udacity is doing as of 2022.
www.investopedia.com/articles/investing/042815/how-coursera-works-makes-money.asp has a good mention:and it links to: www.freecodecamp.org/news/massive-open-online-courses-started-out-completely-free-but-where-are-they-now-1dd1020f59/, very good article!
MOOCs were first created by people with utopian visions for the internet. This means the idea for platforms like Coursera was likely conceived without a business plan in mind. Nonetheless, Coursera has managed to monetize its platform. It is worth noting, however, that monetization has lead to the effective elimination of the original MOOC idea, which is predicated on ideals like free and open access, as well as the building of online communities.
That is a fundamental guiding principle of OurBigBook.com. The educational content must be licensed CC BY-SA!
Perhaps the most reliable way of reaching this state is E-learning websites must allow students to create learning content.
Bibliography:
- academia.stackexchange.com/questions/86179/is-it-financially-worth-it-to-teach-a-mooc-e-g-coursera Is it financially worth it to teach a MOOC (e.g. Coursera)?
- www.classcentral.com/about amazing, they can make money just from ads! I wouldn't expect that they could scale like TripAdvisor, because travelling means very local knowledge, I would expect there to be much fewer MOOCs and for them to be more easily findable on Google. Good thing though, this website.
Ciro Santilli distinctly remembers being taught that at basic electrical engineering school during Ciro Santilli's undergrad studies at the University of São Paulo.
It really allows you to do alternating current calculations much as you'd do DC calculations with resistors, quite poweful. It must have been all the rage in the 1950s.
As of the 20th century, this can be described well as "the phenomena described by Maxwell's equations".
Back through its history however, that was not at all clear. This highlights how big of an achievement Maxwell's equations are.
Our minimal definition of "electronic money" is the following.
Instead of creating legal tender such as Dollars as banknotes or transactions in some complex obscure banking system, the government offers an official simple centralized API that represents it instead.
Each citizen or legal entity has an account there, and transfers between registered users are just simple API calls.
Java is good.
Its boilerplate requirement is a pain, but the design is otherwise very clean.
But its ecosystem sucks.
The development process is rather closed, the issue tracker obscure.
And above all, Google LLC v. Oracle America, Inc. killed everybody's trust in it once and for all. Thanks Oracle.
Oscillators: RC, LC, Crystal by GreatScott! (2015)
Source. Good video. Contains actual breadboard experiments on oscilloscope and circuit diagrams- youtu.be/eYVOdlK15Og?t=66 RC oscillator on breadboard. Produces rectangular wave. Mentions popular integrated circuit that does it: 555 timer IC.
- youtu.be/eYVOdlK15Og?t=175 LC oscillators allows for higher frequencies. Produces sinusoidal output on MHz range. Uses an amplifier to feed back into input and maintain same voltage. Hard to make reliably on breadboard.
- youtu.be/eYVOdlK15Og?t=315 crystal oscillator. Mentions it acts like an LC oscillators. Shows and equivalent model. Wish he had talked more about them. You need support components around it: similarly to the LC case, the amplifier is generally not packaged in.
The language all browsers converted to as of 2019, and therefore the easiest one to distribute and most widely implemented programming language.
Hopefully will be killed by WebAssembly one day.
Because JavaScript is a relatively crap/ad-hoc language, it ended up some decent tooling to make up for that, e.g. stuff like linting via ESLint and reformatting through Prettier is much more widespread than in other languages.
JavaScript data structure are also quite a bit anemic, which makes libraries such as lodash incredibly popular. But most of that stuff should be in the stdlib.
Our JavaScript examples can be found at:
- Node.js example: examples that don't interact with any browser feature. We are just testing those on the CLI which is much more convenient.
- JavaScript browser example: examples that interact with browser-specific features, notably the DOM
- js/confirm-close.html: stackoverflow.com/questions/7317273/warn-user-before-leaving-web-page-with-unsaved-changes
- web-cheat/js-image-load.html: load an image from JavaScript dynamically: stackoverflow.com/questions/226847/what-is-the-best-javascript-code-to-create-an-img-element
- web-cheat/js-image-load-viewport.html: load an image from JavaScript dynamically when it would become visible on the viewport: stackoverflow.com/questions/2321907/how-do-you-make-images-load-only-when-they-are-in-the-viewport
- html/img-load-lazy.html: stackoverflow.com/questions/2321907/how-do-you-make-images-load-lazily-only-when-they-are-in-the-viewport/57389607#57389607
- web-cheat/esm.html: ESM modules
- js/keydown.html: stackoverflow.com/questions/16006583/capturing-ctrlz-key-combination-in-javascript
External libraries
- Text editors
- Interactive HTML table sorting
I would also increase voter percentage due to convenience, and reduce the weight of voting fraud cases, as everyone would be able to check that their own vote was counted correctly.
And then, we would be able to have referendums for basically any important decision being made. No need to go out on the streets and waste your time in a mass protest! Just vote!
It is possible to implement anonymous electronic voting with ring signatures, an algorithm also used by Monero, an anonymity focused cryptocurrency, as mentioned e.g. on this 2004 paper eprint.iacr.org/2004/281.pdf. The system can be set in a way such that you can only deanonymize someone if everyone else, or a very large number of people, conspire against that person.
The same system could also be used to setup forums where only citizens of the country could comment and propose changes and vote on them.
With electronic voting, we could have a system where you can let someone you trust vote for you automatically, or vote automatically for certain subjects alone, a bit like we do by electing senators. But then you would also be able to override specific votes if you wanted to.
In this system therefore, anyone who can proxy vote has to have their vote public, and placed in a decent website that shows clearly who voted for what.
Related:
- www.vote-coin.com/ allows you to delegate your voting power to someone else, that's perfect!
Electroweak Theory and the Origin of the Fundamental Forces by PBS Space Time (2020)
Source. Unsatisfactory, as usual.Experiments to measure it:
The 2019 redefinition of the SI base units defines it precisely and uses it as a measure of charge: en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units#Ampere
Ciro's 2020 perfect Friday evening: jazz fusion + study quantum field theory on an Amazon Kindle. Ahhhhhh.
Running:gives:
hd hello_world.out00000000 7f 45 4c 46 02 01 01 00 00 00 00 00 00 00 00 00 |.ELF............|
00000010 02 00 3e 00 01 00 00 00 b0 00 40 00 00 00 00 00 |..>.......@.....|
00000020 40 00 00 00 00 00 00 00 10 01 00 00 00 00 00 00 |@...............|
00000030 00 00 00 00 40 00 38 00 02 00 40 00 06 00 03 00 |....@.8...@.....|
00000040 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 |................|
00000050 00 00 40 00 00 00 00 00 00 00 40 00 00 00 00 00 |..@.......@.....|
00000060 d7 00 00 00 00 00 00 00 d7 00 00 00 00 00 00 00 |................|
00000070 00 00 20 00 00 00 00 00 01 00 00 00 06 00 00 00 |.. .............|
00000080 d8 00 00 00 00 00 00 00 d8 00 60 00 00 00 00 00 |..........`.....|
00000090 d8 00 60 00 00 00 00 00 0d 00 00 00 00 00 00 00 |..`.............|
000000a0 0d 00 00 00 00 00 00 00 00 00 20 00 00 00 00 00 |.......... .....|
000000b0 b8 01 00 00 00 bf 01 00 00 00 48 be d8 00 60 00 |..........H...`.|
000000c0 00 00 00 00 ba 0d 00 00 00 0f 05 b8 3c 00 00 00 |............<...|
000000d0 bf 00 00 00 00 0f 05 00 48 65 6c 6c 6f 20 77 6f |........Hello wo|
000000e0 72 6c 64 21 0a 00 2e 73 79 6d 74 61 62 00 2e 73 |rld!...symtab..s|
000000f0 74 72 74 61 62 00 2e 73 68 73 74 72 74 61 62 00 |trtab..shstrtab.|
00000100 2e 74 65 78 74 00 2e 64 61 74 61 00 00 00 00 00 |.text..data.....|
00000110 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
*
00000150 1b 00 00 00 01 00 00 00 06 00 00 00 00 00 00 00 |................|
00000160 b0 00 40 00 00 00 00 00 b0 00 00 00 00 00 00 00 |..@.............|
00000170 27 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |'...............|
00000180 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
00000190 21 00 00 00 01 00 00 00 03 00 00 00 00 00 00 00 |!...............|
000001a0 d8 00 60 00 00 00 00 00 d8 00 00 00 00 00 00 00 |..`.............|
000001b0 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
000001c0 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
000001d0 11 00 00 00 03 00 00 00 00 00 00 00 00 00 00 00 |................|
000001e0 00 00 00 00 00 00 00 00 e5 00 00 00 00 00 00 00 |................|
000001f0 27 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |'...............|
00000200 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
00000210 01 00 00 00 02 00 00 00 00 00 00 00 00 00 00 00 |................|
00000220 00 00 00 00 00 00 00 00 90 02 00 00 00 00 00 00 |................|
00000230 08 01 00 00 00 00 00 00 05 00 00 00 07 00 00 00 |................|
00000240 08 00 00 00 00 00 00 00 18 00 00 00 00 00 00 00 |................|
00000250 09 00 00 00 03 00 00 00 00 00 00 00 00 00 00 00 |................|
00000260 00 00 00 00 00 00 00 00 98 03 00 00 00 00 00 00 |................|
00000270 4c 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |L...............|
00000280 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
00000290 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
000002a0 00 00 00 00 00 00 00 00 00 00 00 00 03 00 01 00 |................|
000002b0 b0 00 40 00 00 00 00 00 00 00 00 00 00 00 00 00 |..@.............|
000002c0 00 00 00 00 03 00 02 00 d8 00 60 00 00 00 00 00 |..........`.....|
000002d0 00 00 00 00 00 00 00 00 01 00 00 00 04 00 f1 ff |................|
000002e0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
000002f0 11 00 00 00 00 00 02 00 d8 00 60 00 00 00 00 00 |..........`.....|
00000300 00 00 00 00 00 00 00 00 1d 00 00 00 00 00 f1 ff |................|
00000310 0d 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................|
00000320 00 00 00 00 04 00 f1 ff 00 00 00 00 00 00 00 00 |................|
00000330 00 00 00 00 00 00 00 00 2d 00 00 00 10 00 01 00 |........-.......|
00000340 b0 00 40 00 00 00 00 00 00 00 00 00 00 00 00 00 |..@.............|
00000350 34 00 00 00 10 00 02 00 e5 00 60 00 00 00 00 00 |4.........`.....|
00000360 00 00 00 00 00 00 00 00 40 00 00 00 10 00 02 00 |........@.......|
00000370 e5 00 60 00 00 00 00 00 00 00 00 00 00 00 00 00 |..`.............|
00000380 47 00 00 00 10 00 02 00 e8 00 60 00 00 00 00 00 |G.........`.....|
00000390 00 00 00 00 00 00 00 00 00 68 65 6c 6c 6f 5f 77 |.........hello_w|
000003a0 6f 72 6c 64 2e 61 73 6d 00 68 65 6c 6c 6f 5f 77 |orld.asm.hello_w|
000003b0 6f 72 6c 64 00 68 65 6c 6c 6f 5f 77 6f 72 6c 64 |orld.hello_world|
000003c0 5f 6c 65 6e 00 5f 73 74 61 72 74 00 5f 5f 62 73 |_len._start.__bs|
000003d0 73 5f 73 74 61 72 74 00 5f 65 64 61 74 61 00 5f |s_start._edata._|
000003e0 65 6e 64 00 |end.|
000003e4hello_world.asm
section .data
hello_world db "Hello world!", 10
hello_world_len equ $ - hello_world
section .text
global _start
_start:
mov rax, 1
mov rdi, 1
mov rsi, hello_world
mov rdx, hello_world_len
syscall
mov rax, 60
mov rdi, 0
syscallCompiled with:
nasm -w+all -f elf64 -o 'hello_world.o' 'hello_world.asm'
ld -o 'hello_world.out' 'hello_world.o' Unlisted articles are being shown, click here to show only listed articles.