Matrix congruence can be seen as the change of basis of a bilinear form Updated 2025-07-01 +Created 1970-01-01
From effect of a change of basis on the matrix of a bilinear form, remember that a change of basis modifies the matrix representation of a bilinear form as:
So, by taking , we understand that two matrices being congruent means that they can both correspond to the same bilinear form in different bases.
Many subjects have changed very little in the last hundred years, and so it is mind-blowing that people have to pay for books that teach them!
Since Ciro Santilli was young, he has been bewildered by the natural sciences and mathematics due to his bad memory.
The beauty of those subjects has always felt like intense sunlight in a fresh morning to Ciro. Sometimes it gets covered by clouds and obscured by less important things, but it always comes back again and again, weaker or stronger with its warmth, guiding Ciro's life path.
As a result, he has always suffered a lot at school: his grades were good, but he wasn't really learning those beautiful things that he wanted to learn!
First, before university, school organization had only one goal: put you into the best universities, to make a poster out of you and get publicity, so that more parents will be willing to pay them money to put their kids into good university.
Ciro once asked a chemistry teacher some "deeper question" after course was over, related to the superficial vision of the topic they were learning to get grades in university entry exams. The teacher replied something like:Ciro feels that this was one of the greatest compliments he has ever received in his life. This teacher, understood him. Funny how some things stick, while all the rest fades.
You remind me of a friend of mine. He always wanted to understand the deeper reason for things. He now works at NASA.
Another interesting anecdote is how Ciro Santilli's mother recalls that she always found out about exams in the same way: when the phone started ringing as Ciro's friends started asking for help with the subjects just before the exam. Sometimes it was already too hopelessly late, but Ciro almost always tried. Nothing shows how much better you are than someone than teaching them.
Then, after entering university, although things got way better because were are able to learn things that are borderline useful.
Ciro still felt a strong emotion of nostalgia when after university his mother asked if she could throw away his high school books, and Ciro started tearing them all down for recycling. Such is life.
University teachers were still to a large extent researchers who didn't want to, know how to and above all have enough time and institutional freedom to teach things properly and make you see their beauty, some good relate articles:
The very fact that you had very little choice of what to learn so that a large group can get a "Diploma", makes it impossible for people to deeply learn what the really want.
This is especially true because Ciro was in Brazil, a third world country, where the opportunities are comparatively extremely limited to the first world.
Also extremely frustrating is how you might have to wait for years to get to the subject you really want. For example, on a physics course, quantum mechanics is normally only taught on the third year! While there is value to knowing the pre-requisites, holding people back for years is just too sad, and Ciro much prefers backward design. And just like the university entry exams, this creates an entry barrier situation where you might in the end find that "hey, that's not what I wanted to learn after all", see also: students must have a flexible choice of what to learn.
We've created a system where people just wait, and wait, and wait, never really doing what they really want. They wait through school to get into university. They wait through university to get to masters. They wait through masters to get to PhD. They wait through PhD to become a PI. And for the minuscule fraction of those that make it, they become fund proposal writers. And if you make any wrong choice along the, it's all over, you can't continue anymore, the cost would be too great. So you just become software engineer or a consultant. Is this the society that we really want?
And all of this is considering that he was very lucky to not be in a poor family, and was already in some of the best educational institutions locally available already, and had comparatively awesome teachers, without which he wouldn't be where he is today if he hadn't had such advantages in the first place.
But no matter how awesome one teacher is, no single person can overcome a system so large and broken. Without technological innovation that is.
The key problem all along the way is the Society's/Government's belief that everyone has to learn the same things, and that grades in exams mean anything.
Even if you wanted to really learn natural sciences and had the time available, it is just too hard to find good resources to properly learn it. Even attending university courses are hit and miss between amazing and mediocre teachers.
If you go into a large book shop, the science section is tiny, and useless popular science books dominate it without precise experiment descriptions. And then, the only few "serious" books are a huge list of formulas without any experimental motivation.
And if you are lucky to have access to an university library that has open doors, most books are likely to be old and boring as well. Googling for PDFs from university courses is the best bet.
Around 2012 however, he finally saw the light, and started his path to Ciro Santilli's Open Source Enlightenment. University was not needed anymore. He could learn whatever he wanted. A vision was born.
To make things worse, for a long time he was tired of seeing poor people begging on the streets every day and not doing anything about it. He thought:which like everything else is likely derived subconsciously from something else, here Schindler's list possibly adapted quote from the Talmud:
He who teaches one thousand, saves one million.
So, by the time he left University, instead of pursuing a PhD in theoretical Mathematics or Physics just for the beauty of it as he had once considered, he had new plans.
We needed a new educational system. One that would allow people to fulfill their potential and desires, and truly improve society as a result, both in rich and poor countries.
And he found out that programming and applied mathematics could also be fun, so he might as well have some fun while doing this! ;-)
So he started Booktree in 2014, a GitLab fork, worked on it for an year, noticed the approach was dumb, and a few years later started building this new version. The repo github.com/booktree/booktree is a small snapshot of Ciro's 2014 brain on the area, there were quite a few similar projects at the time, and most have died.
Ciro is basically a librarian at heart, and wants to be the next:
- Jimmy Wales
- Brewster Kahle
- Tim Berners Lee
- Tim O'Reilly, who once brilliantly described O'Reilly Media as "a lifestyle business that got out of control" [ref]
- Aaron Swartz. Minus suicide hopefully.
"Jimmy Wales: How a ragtag band created Wikipedia" 2005 TED talk
. Source. Original source: www.ted.com/talks/jimmy_wales_the_birth_of_wikipedia.!!! Survivorship bias alert !!!
quoteinvestigator.com/2018/05/07/overcome/
If you want to do something, but you are afraid to do it, then that is likely what you should do.
www.goodreads.com/quotes/50458-whatever-you-re-meant-to-do-do-it-now-the-conditions Doris Lessing:
Whatever you're meant to do, do it now. The conditions are always impossible.
For example, when Ciro Santilli was deciding what to do in university, he wanted mostly to do pure physics.
But because he was afraid he was going to die poor and unemployed because of that, he picked engineering instead.
That was a mistake.
His family was not even poor. He was young and did not have a family to support. His father even told him: "do whatever the fuck you want, we support your decision".
But he was a coward.
It was also in part because a physicist uncle which he respected suggested that as an engineer Ciro might be able to make useful contributions to tooling required by physics. When Roberto Salmeron died in 2020, Ciro's friends shared this 2013 video interview with the late professor, where he explains he first went to the University of São Paulo to study engineering (like Ciro), but then fell for his passion for physics (like Ciro?), his first task being to build a Geiger counter, thus explaining the likely origin of the uncle's theory. But who knows, maybe he was right. Maybe Ciro's OurBigBook.com will become huge and help a lot of people, and it might not have had Ciro not done engineering and learnt programming. Destiny operates in weird ways sometimes.
Furthermore, while in University, Ciro learnt about the molecular Sciences Course of the University of São Paulo, a fantastic sounding full time course that any student could transfer to called that teaches various natural sciences topics which Ciro loves (Mathematics, Physics, Chemistry, Biology) and which students from the entire university can apply to transfer to only after joining the university, with the guarantee that they can go back to their original courses if they didn't adapt to the new course.
But did Ciro do it? Nope, he remained an even larger coward.
Had he studied more sciences, he might have been happier, and might have had greater achievements later in life, in particular when he went to École Polytechnique.
Similar thoughts crossed his mind when he started his campaign for freedom of speech in China, but this time he had learnt the lesson, and went for it, and it felt very good.
If you have a day job, but also have a dream, and want to keep the day job for a reason, try to reserve the time of the day that your brain works best before or after work for your dream: do one cool thing every day.
Companies can help you grow because you see real problems from within them, but their end goal is to consume you as much as possible. Don't let that happen. Invest part of what you gain, in yourself. www.outsideonline.com/outdoor-adventure/paradox-going-outside/ The Paradox of Going Outside by James Somers (2012) puts it incredibly well:
I work, for instance, as a Web developer. It's a very good job. Our office is a block south of Union Square, a 12-minute commute from my apartment. We're served breakfast every morning. Our kitchen is stocked with "provisions" of organic beef jerky, coconut water, craft beers, chips, and two restaurant-class espresso machines. We have two ping pong tables and buckets of 3-star ping pong balls. (A new office manager bought "1-stars" once and some of the guys protested by crushing them.) We work on 4-cored Apple Mac computers with dual monitors. We have an unmolested hour for lunch, 10-minute breaks in the morning and afternoon, and a "do not disturb" policy past the working hours. We even have a specific email address where employees can ask for free things: genuine maple syrup, hot chocolate, a $900 chair, a new keyboard. Most of the programmers make six figures, and many of those have only three or four years of experience.It's impossible to say so without sounding like the spokesperson for Entitlement itself but working there is still sort of soul-crushing. It's soul-crushing in the way that any job that doesn't command your full passionate attention must be. What happens is that I will be in my chair in the early afternoon and I will accidentally step out of myself and all I'll see is time passing, nine-hour parcels of healthy consciousness forever being packed away as the user experience of clerical workers or consumers or whoever gets marginally better; and I'll end up thinking that this enterprise of mine is not so much creative but bureaucratic, that what I've gotten good at is reading the instruction manuals of other people, finding my way around their insignificant warrens. And in those moments the whole business will seem to me like kind of a tragic waste.
Other quotes:
- is a phrase Sergey Brin uses. The Google Story claims he picked that up from academia, and quotes this from a september 2003 talk in an Israeli elite high school.
Healthy Disregard For The Impossible
- quoteinvestigator.com/2014/05/29/find-love/
Find What You Love and Let It Kill You
- Cute boy things by Caroline Ellison:
if you are a boy with the confidence to advocate for unconventional ideas and take actions based on them you are valid
- How can I be as great by Justine Musk:
rock the boat
- From the 1922 poem Portuguese Sea by famous Portuguese poet Fernando Pessoa, which gets drilled into the head of every Brazilian high school student:He who wants to pass beyond the Bojador
Must go beyond pain.Quem quer passar além do Bojador
Tem que passar além da dor. - Translation of a poem by Muhammad Iqbal TODO date:One is reminded of As iron sharpens iron, so one person sharpens another.
- "NPC life" as a way to refer to a soul crushing job
- twitter.com/0xTenkito/status/1775167216641548732, a cryptocurrency investor says:However there is one thing to lose, if you do safer investments and don't lose everything, then you might be able to retire earlier.
- archive.ph/mlaLK
- twitter.com/0xTenkito/status/1775167216641548732, a cryptocurrency investor says:
Dilbert "A small brain irrationally puts more weight on a small loss than on a huge opportunity" cartoon (2000)
Source. 
Jake Likes Onions "Slowly" cartoon
. Source. This is what trying to reach a dream part time feels like. The cartoon reads: "The tiger pursues its prey. Slowly. The human pursues its life goals. Slowly. Very slowly.".Excerpt from the documentary film "Steve Jobs: Secrets of Life" (1994)
Source. When you grow up you tend to get told that the world is the way it is and your life is just to live your life inside the world. Try not to bash into the walls too much. Try to have a nice family life, have fun, save a little money. That's a very limited life. Life can be much broader once you discover one simple fact: Everything around you that you call life was made up by people that were no smarter than you. And you can change it, you can influence it... Once you learn that, you'll never be the same again.
Of course, survivorship bias alert!
What Would You Do If Money Were No Object by Alan Watts
. Source. Sample transcription: genius.com/Alan-watts-what-if-money-was-no-object-annotated:What do you desire? What makes you itch? What sort of a situation would you like?Let's suppose, I do this often in vocational guidance of students, they come to me and say, well, "we're getting out of college and we have the faintest idea what we want to do". So I always ask the question, "what would you like to do if money were no object? How would you really enjoy spending your life?"Well, it's so amazing as a result of our kind of educational system, crowds of students say well, we'd like to be painters, we'd like to be poets, we'd like to be writers, but as everybody knows you can't earn any money that way. Or another person says well, I'd like to live an out-of-doors life and ride horses. I said you want to teach in a riding school?Let's go through with it. What do you want to do? When we finally got down to something, which the individual says he really wants to do, I will say to him, you do that and forget the money, because, if you say that getting the money is the most important thing, you will spend your life completely wasting your time. You'll be doing things you don't like doing in order to go on living, that is to go on doing things you don't like doing, which is stupid. Better to have a short life that is full of what you like doing than a long life spent in a miserable way.And after all, if you do really like what you're doing, it doesn't matter what it is, you can eventually turn it - you could eventually become a master of it. It's the only way to become a master of something, to be really with it. And then you'll be able to get a good fee for whatever it is. So don't worry too much. That's everybody is - somebody is interested in everything, anything you can be interested in, you will find others will.But it's absolutely stupid to spend your time doing things you don't like, in order to go on spending things you don't like, doing things you don't like and to teach our children to follow in the same track. See what we are doing, is we're bringing up children and educating to live the same sort of lives we are living. In order that they may justify themselves and find satisfaction in life by bringing up their children to bring up their children to do the same thing, so it's all retch and no vomit. It never gets there. And so, therefore, it's so important to consider this question: What do I desire?
Keep Chargin' from a Show of Hands by Victor Wooten (1996)
Source. That's the way I live my life, I give it my all. I think that a person should really make up his mind what he wants to do, and when did made up, he cannot fail at it. The basic rule to sucess I think, is when the going gets tough, that is a positive signal to keep chargin'.
Charles Bukowski is one of the most hardcore don't be a pussy people ever. It's almost scary. Far beyond Ciro level.
thebestamericanpoetry.typepad.com/the_best_american_poetry/2008/11/the-laughing-he.html
your life is your life
don't let it be clubbed into dank submission.
be on the watch.
there are ways out.
there is light somewhere.
it may not be much light but
it beats the darkness.
be on the watch.
the gods will offer you chances.
know them.
take them.
you can't beat death but
you can beat death in life, sometimes.
and the more often you learn to do it,
the more light there will be.
your life is your life.
know it while you have it.
you are marvelous
the Gods wait to delight
in you.
www.goodreads.com/quotes/39207-if-you-re-going-to-try-go-all-the-way-otherwise
If you're going to try, go all the way. Otherwise, don't even start. This could mean losing girlfriends, wives, relatives and maybe even your mind. It could mean not eating for three or four days. It could mean freezing on a park bench. It could mean jail. It could mean derision. It could mean mockery--isolation. Isolation is the gift. All the others are a test of your endurance, of how much you really want to do it. And, you'll do it, despite rejection and the worst odds. And it will be better than anything else you can imagine. If you're going to try, go all the way. There is no other feeling like that. You will be alone with the Gods, and the nights will flame with fire. You will ride life straight to perfect laughter. It's the only good fight there is.
I have one of two choices - stay in the post office and go crazy... or stay out here and play at writer and starve. I have decided to starve.
Bukowski kissing his typewriter.
Like Ciro Santilli and his computer!All adults are bored scene from an Edward Teller, An Early Time
. Source. Up to the time that I met Klug ([a mathematiciam]), I was sure that all grown ups were people to be pitied. They had to work, they were tired, they were bored with what they were doing. I heard both my parents often complain. Klug was the first man whom I met who most obviously enoyed what he was doing.
There are unlisted articles, also show them or only show them.