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The Matrix Cookbook (2012) [pdf] (uwaterloo.ca)
254 points by wewake 55 days ago | hide | past | web | favorite | 39 comments



"Neo's Noodle Soup"

In a large pot over medium heat, melt butter. Cook onion and celery in butter until just tender, 5 minutes.

Pour in chicken and vegetable broths and stir in chicken, noodles, carrots, basil, oregano, salt and pepper.

Bring to a boil, then reduce heat and simmer 20 minutes before serving.

There is no spoon.


You had me at "butter".


I'm disappointed. I was expecting a recipe for the goo that Neo was forced to eat in the first movie.


Or recipes that make everything taste like chicken


Got me through my first machine learning class, highly recommend!


I very much like the form of this, yet I wish that the dependencies were ordered differently, such that one would not need to jump around (e.g. eigenvalues before determinants, since the latter are defined by the former).


The author's email address is in there and it sounds like they were soliciting for comments... who knows if they are still maintaining this or not.


This is intended as a reference, not as a teaching tool, so I think the order it is currently in works fine.

Edit: Sorry, I misinterpreted the order of your suggested change. I agree that, even for use as a reference, perhaps the order could be improved.


I’ve been brushing up my Calculus and Linear Algebra, and this will help immensely. Thanks!


Worth checking the Wikipedia page on matrix calculus to see which version of the notation you use! This is in numerator (iirc) and so d (vec x) / d(t) = (vec x). I was used to d (vec x) / d(t) = transpose(vec x), and so this cookbook confused me for ages :S


When I learned about matrices in school it really bored me, even though math in general really captures my interest. Can anyone recommend a good source that makes matrices interesting and captivating?


3 Blue 1 Brown has a much better introduction than any course I've seen: http://www.3blue1brown.com/essence-of-linear-algebra-page/


Say you start with a small system of equations and you find out how you can solve them. Then you solve a bunch more, but then you start to notice that you don't like writing out the x, y, and z's, so you just keep the coefficients, in a box of sorts. Then you translate what you were doing into operations on the rows of this ... matrix you call it. After solving some more equations, you start to forget where these things come from. Surely they come from equations, but because the coefficients, plus signs and equal signs disappear, you are left with a box of numbers really.

What happens next is that different questions start to come to mind. The matrix attains a life of its own. You start to think questions like "Well, we have some x, y, z's and this box of numbers somehow transforms them into the right hand side's a, b, c's". Ok, the matrix is some kind of "transformation" now. You look at its properties. It appears that aX + bY can be computed entry-wise, so maybe this is a fundamental property and you call it linearity. Hmm. At some point you forget about the boxes of numbers and now you have bonafide transformations. From what? To where? You call these...vector spaces. And so on.

Further down the line you become preoccupied by questions of a different flavour, like what happens if you want something like Ax = cx. That is, we get x back with minimal distortion. Fairly simple question that leads to a lot of math.

It also just happens that when you consider mathematical functions of several dimensions, and matrices become apparent when you consider linear approximations. You've built this great theory for them and now that theory seems to really help in these kinds of problems. That is, a LOT of computational problems in this world.


Matrices are mathematical batch processing.

The expressiveness and power you get from being able to cast and solve problems in matrix form is similar to the lightbulb that pops up when one “gets” the relational algebraic power underpinning SQL.


Matrices become captivating when you try to do almost any kind of engineering thing in the real world.

Like building a graphics or physics engine, or calculating the Page Rank of a web page, etc'.

If you can program, I recommend trying to build a 2D graphics and physics engine using vectors to represent position and velocity.

Also, Steven Wittens is amazing: http://acko.net/tv/webglmath/


I am amazed that so many people honestly expected a cookbook for meals in the movie 'the matrix'...


Super cool! Thanks for sharing!


can't connect to the server as it doesn't have TLS 1.2


TL; DR:

What is this? These pages are a collection of facts (identities, approximations, inequalities, relations, ...) about matrices and matters relating to them. It is collected in this form for the convenience of anyone who wants a quick desktop reference.

In case you were, uh, expecting to see Keanu Reeves in a kitchen apron.


Thanks. I was just now straining to remember what food was shown in the films. A bowl of snot. A juicy & delicious steak. The oracle's cookies. I actually never realized before that food is such a theme. Makes sense, it is a very non-machine activity to consume food.



> Makes sense, it is a very non-machine activity to consume food.

Dang. Now I feel like running a GAN to come up with new recipes!



Obligatory XKCD https://xkcd.com/720/


How can you forget the slice of cake that the merovingian reprogrammed?


Prefer not to think of the sequels if possible.


I was expecting the recipes for the "protein shake" they eat in the Nebuchadnezzar and Cypher's steak :(

for like minded people: https://youtu.be/eA6uLMsl9w0


Personally I was expecting linear-algebra based recipes that let you vary proportions continuously or something.


I only ever took one course in university on linear algebra and numerical methods, and I'm an electronic engineering student. But my hobbies (mathematical classical and Marxian economics) necessitate a deep understanding of matrices, sets and vector algebra. I hope this will help me!


Dang it! I thought this was gonna be a cookbook from the movie Matrix. Like how to bake the cookies the oracle made, or the steak Cypher ate. That looked good.



Ignorance is bliss.


Cypher, is that you?


I expected a deep rundown of the glop and what it would take for it to be all you need.


i am so disappointed when i find out it is matrix the mathematics!


The Architect approves. If only Neo was a linear algebra problem, and Smith wasn't an unforeseen variable the Oracle snuck in there!


I often say: "If Neo had simply read Linear Algebra textbooks instead of hacking around all night long, we would have known that the matrix is a representation of a linear map (morphism of vector spaces) with respect to given bases in the domain and codomain.".

Mathematics lets you see and understand the matrix.


Also perplexed and disappointed with the linked .pdf :(


Now I know matrix.




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