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- 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
See also: e-learning website.
Whenever Ciro Santilli walks in front of a school and sees the tall gates it makes him sad. Maybe 8 year olds need gates. But do we need to protect 15 year olds like that? Students should be going out to see the world, both good and evil not hiding from it! We should instead be guiding them to the world. But instead, we are locking them up in brainwashing centers.
Video "The Purpose of Education by Noam Chomsky (2012)" puts it well, education can be either be:He has spoken about that infinitely, e.g. from when he was thin: www.youtube.com/watch?v=JVqMAlgAnlo
- a brainwashing to make people comply with The Establishment
- a way to get people genuinely interested and help them to reach their life goals
Bibliography:
- www.youtube.com/watch?v=ts7CEFQM2bE How Education Became Indoctrination: Dr Stephen Hicks (2021) Interview by www.youtube.com/c/KnowlandKnows Interesting channel. "Are you sick of woke-washing in education? Free speech distinguishes education from indoctrination" and "I taught at Eton College before I was fired because 'The Patriarchy Paradox' caused offence.".
Diodes Explained by The Engineering Mindset (2020)
Source. Good video:- youtu.be/Fwj_d3uO5g8?t=153 how it works
- youtu.be/Fwj_d3uO5g8?t=514 applications:
- protection against accidental battery inversion
- rectifiers, notably mentions a diode bridge
Many/most microcontroller boards have analog-to-digital converters built into them, it is very convenient. E.g. it is the case for the Raspberry Pi Pico.
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . 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. 
- 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