Is it mega fast? Nope
Does it work? Yup.
For positive definite matrices only.
TODO application.
www.studentclustercompetition.us/ comments:
The HPCG benchmark uses a preconditioned conjugate gradient (PCG) algorithm to measure the performance of HPC platforms with respect to frequently observed but challenging patterns of computing, communication, and memory access. While HPL provides an optimistic performance target for applications, HPCG can be considered as a lower bound on performance. Many of the top 500 supercomputers also provide their HPCG performance as a reference.
- math.stackexchange.com/questions/23312/what-is-the-importance-of-eigenvalues-eigenvectors/3503875#3503875
- math.stackexchange.com/questions/1520832/real-life-examples-for-eigenvalues-eigenvectors
- matheducators.stackexchange.com/questions/520/what-is-a-good-motivation-showcase-for-a-student-for-the-study-of-eigenvalues
Every invertible matrix can be written as:where:Note therefore that this decomposition is unique up to swapping the order of eigenvectors. We could fix a canonical form by sorting eigenvectors from smallest to largest in the case of a real number.
- is a diagonal matrix containing the eigenvalues of
- columns of are eigenvectors of
Intuitively, Note that this is just the change of basis formula, and so:
- changes basis to align to the eigenvectors
- multiplies eigenvectors simply by eigenvalues
- changes back to the original basis
ASCII art of a Force of Will, a famous and powerful Magic: The Gathering card first printed in 1996.
This is Ciro Santilli's personal favorite ASCII art he has found in the blockchain so far. Also Ciro could not find any other previous source of this, so there is some chance it is original. One can dream.
The choice of card is probably linked to the function of the card in the game of Magic: The Gathering. This card essentially prevents the opponent from casting a spell they are about to cast. The presumed intended meaning of this art is further accentuated by the old card type term "interrupt" (late renamed to "instant"), which suggests that "this ASCII art is an interruption to the normal monetary transactions of the blockchain".
One of also reminded of the prayer wars interruption attempts. We could not however identify anything specific that this ASCII art might have tried to interrupt besides the normal flow of monetary transactions.
If one goes full art critic mode, it is also tempting to draw a parallel between the card's "You may pay 1 life" alternative casting cost (as opposed to 5 mana, 3 and two blue, which is a very large cost for most games) as being a reference to the money spent by the uploader of the art to upload it.
TODO understand exactly how it was encoded and why it is so weird. The
UUUU has a slightly weird encoding which we fixed by hand here TODO understand. -------------------------------------
| Force of Will 3 U U |
| --------------------------------- |
| | //////////// | |
| | ////() ()\////\ | |
| | ///_\ (--) \///\ | |
| | ) //// \_____///\\ | |
| | ) \ / / / / | |
| | ) / \ | | / _/ | |
| | ) \ ( ( / / / / \ | |
| | / ) ( ) / ( )/( ) \ | |
| | \(_)/(_)/ /UUUU \ \\\/ | | |
| .---------------------------------. |
| Interrupt |
| ,---------------------------------, |
| | You may pay 1 life and remove a | |
| | blue card in your hand from the | |
| | game instead of paying Force of | |
| | Will's casting cost. Effects | |
| | that prevent or redirect damage | |
| | cannot be used to counter this | |
| | loss of life. | |
| | Counter target spell. | |
| `---------------------------------` |
| l
| Illus. Terese Nelsen |
-------------------------------------
Force of Will Magic: The Gathering card (Alliances)
Source. A high resolution scan of the original card depicted in the ASCII art for comparison.The following two ASCII transactions:suggest this ASCII art might have been uploaded by Figure "Erich Erstu", AKA Hyena, creator of cryptograffiti.info, a service which would have allowed uploading ASCII content to the blockchain.
tx 0f05c47a8caafadecc10d70ba3bf010eaf6bb416b5e1ad7b01cf3445f5fb7a1c
I am. Therefore, I have come to be.
-- Hyena
tx e6d48f6912929a58a2ee30c13768058777d8547215c27109b5cb0724e7abaaba
Erich,
Bro, this looks excellent!!
-DurielThe only other mention of "Duriel" in the blockchain is tx 140562ceb42fc8943fa52ccc0ddbb11ca2d88dae9b5240d7a4b46864538c515a which has some freedom of speech comments and gives the email:paystamper.com was some other blockchain service from circa 2015:
Duriel@paystamper.com = 1HcuhfTAiQCt6KdMG2rZLXsTcKYj9nLDhSAll found so far are also reproduced at: asciiart.website/index.php?art=people/naked%20ladies therefore not blockchain original.
- tx 9206ec2a41846709a59cafb406dd7b07082bfc27664bbc5c6d4df310c1e1b91f block 290848 (2014-03-16) via cryptograffiti.info: sexually aroused naked woman sitting looking forward with legs open showing her vagina. Vagina row as an identifier for Ctrl + F:A bit bellow tx 8367a48e4a863e37b3749bc9c111327b07a7c383ec9b3e7ce8d41949e71e1c10 has a large hand showing the middle finger and wearing a watch:
. `. .\x./-`--...../' ; :Reproduced e.g. at: www.textartcopy.com/ascii-middle-finger.html/"\ |\./| | | | | |>~<| | | /'\| |/'\.. /~\| | | | \ [ | | | | \ | | | | | \ | ~ ~ ~ ~ |` ) | / \ / \ / \ / |--//''`\--| | (( +==)) | |--\_|_//--| - tx 0aab36554c2ac5ec23747e7f21f75dbe3f16739134cf44953ad7ac98927146d6 block 322920 (2014-09-28) via cryptograffiti.info: naked woman laying on her side showing her vagina from under her legs, signed
fsc. Vagina row:Fully reproduced e.g. at www.asciiart.eu/people/sexual/women which credits the art to a "Marcin Glinski" (Polish: Marcin Gliński), possibly this dude github.com/silentlamb/ASCII-Arts | www.linkedin.com/in/marcinglinski)The signature is also listed at www.asciiart.eu/ascii-artists/who-is-who for example.`-:/"-7.--"" _::.-'P::.. \} - tx 66826fccef3e3ebb34abce25bfeff8f9dcaaf88e4707a5576c494d8a1cf1681a block 388714 (2015-12-16) has a one liner penis and breasts:soon followed by more breasts at 37c1e90c6ce3e648c51bfa38cbb43e996cd46e038517596d4c90ca2a6425a701:
jEW B====D ( . Y . )Found by Messages from the mines.jEW ( . Y . )TIDDIES( . Y . )
Centralized system that still attempts some level of privacy.
In it, a central bank issue tokens that are stored offline in your cell phone, a bit like cash bank notes.
When you take those tokens, a corresponding amount gets removed from your bank account, a bit like cash bank notes.
When a transaction is made, tokens are put into a spent token list via central API, and cannot be double spent thereafter. The corresponding ammount is then added to the bank account of the receiver. This also means that offline transactions are not possible.
In the classification of finite simple groups, groups of Lie type are a set of infinite families of simple lie groups. These are the other infinite families besides te cyclic groups and alternating groups.
A decent list at: en.wikipedia.org/wiki/List_of_finite_simple_groups, en.wikipedia.org/wiki/Group_of_Lie_type is just too unclear. The groups of Lie type can be subdivided into:
- Chevalley groups
- TODO the rest
The first in this family discovered were a subset of the Chevalley groups by Galois: , so it might be a good first one to try and understand what it looks like.
TODO understand intuitively why they are called of Lie type. Their names , seem to correspond to the members of the classification of simple Lie groups which are also named like that.
But they are of course related to Lie groups, and as suggested at Video "Yang-Mills 1 by David Metzler (2011)" part 2, the continuity actually simplifies things.
Two ways to see it:
- a ring where inverses exist
- a field where multiplication is not necessarily commutative
An algebra over a field where division exists.
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