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The Matrix Cookbook (2012) [pdf]
- porphyra 3y agoThe section on multivariate Gaussians was a real life saver at work recently. Highly recommended!
- yootyootr 3y agoFor those clicking in expecting "Neo's protein porridge," "Morpheus Meatballs," and "Trinity's Tripe," you are going to be disappointed in that this is neither a delicious pop-culture recipe book, nor does it relate to hit Wachowski trilogy "The Matrix."
- bee_rider 3y agoNeo : What are you trying to tell me? That I can dodge ZERO PIVOTS? Morpheus : No, Neo. I'm trying to tell you that when you're ready, YOU’LL HAVE AN SPD MATRIX.
- samstave 3y ago[flagged]
- kemiller2002 3y agoIn the Wachowskis' defense on that one, it would be a really short cookbook. Oatmeal: tastes like chicken. done.
- keiferski 3y ago"It's a single-celled protein combined with synthetic aminos, vitamins and minerals. Everything the body needs."
- __void 3y agoyes I was a little disappointed, ngl a post-apocalyptic recipe book would be really interesting (canned cultivated meat, mycotissues, texturised hydroponic soya and boiled grains, yummm)
- giardini 3y ago__void says: "a post-apocalyptic recipe book...": That would be "To Serve Man": https://en.wikipedia.org/wiki/To_Serve_Man https://en.wikipedia.org/wiki/To_Serve_Man You can view that "Twilight Zone" episode at: https://www.youtube.com/watch?v=wJjvg-Gq1LE https://www.youtube.com/watch?v=wJjvg-Gq1LE
- purpleflame1257 3y agoI actually came in hoping for the chat protocol >_>
- euniceee3 3y agoSame
- cratermoon 3y agoI was at least hoping for a cookie recipe.
- bee_rider 3y agoThere’s also the famous Numerical Recipes book. That is more like a set of steps you can follow when writing your code, which seems like what a recipe/cookbook ought to contain. Since this work is about identities, aka representations that can be swapped in for one another, IMO they should have called it the “matrix ingredient substitution guide.”
- CoastalCoder 3y agoIIRC the Numerical Recipes book was a bit of a copyright Trojan Horse. (I don't know if that's really true, I just heard it mentioned somewhere.) Presumably this book doesn't carry that risk.
- hgsgm 3y agoEverything written is copyrighted, whether it's in a published book or not.
- bee_rider 3y agoI wasn’t aware of the issue, but a Wikipedia seems to indicate that there was a concern that the specific implementations of the algorithms in Numerical Recipes are copyrighted, and there’s always a temptation to copy that sort of thing directly out of the book. The linked PDF here is a big collection of mathematical identities. I’m sure their specific representation in the PDF is copyrighted somehow, but there’s no real temptation to use the representation here, just the mathematical idea.
- eesmith 3y agoNot quite. In the US at least, works by the federal government are not covered under copyright. Nor are 'mere facts' (eg, a complete list of phone numbers and names for a region). See https://en.wikipedia.org/wiki/Copyright_law_of_the_United_States#Works_subject_to_copyright_law https://en.wikipedia.org/wiki/Copyright_law_of_the_United_St... . bee_rider already referred to https://en.wikipedia.org/wiki/Numerical_Recipes#License https://en.wikipedia.org/wiki/Numerical_Recipes#License so I leave it at that.
- liorben-david 3y agoMy favorite matrix problem that I've had to do was showing that when viewed as a function from n^2 Real space to the Real number line, the determinant is continuous and differentiable. Computing its derivative is a particularly satisfying exercise in pattern parsing From that you get that the set of Orthogonal matrices(Matrices with determinant 1) end up forming a manifold
- ineedasername 3y ago[flagged]
- bee_rider 3y agoThe battery thing was the dumbest plot point, which is weird, given that it was in the first movie.
- rcxdude 3y agoIt was executive meddling: the original idea was the machines were using the human's brains as a supercomputer, but it was thought this would be too difficult for audiences to understand.
- bee_rider 3y agoThat would have been a much more sensible reason. My head-canon is that the machines were actually just trying to keep the humans from self-destructing, but supercomputer is a fine answer if we still want the machines to be fundamentally antagonistic towards humanity.
- BizarroLand 3y agoIt was supposed to be storage and processing but the directors thought that viewers wouldn't understand that a human brain could store (what was thought to be at the time) a few terabytes of data, so they dumbed the concept down. It would have made so much more sense that Neo had the ability to manipulate the Matrix because his brain had admin access to it rather than "he's just some super who won the cybergenetic lottery".
- ineedasername 3y agoI never understood why they’d need to keep humans around at all. Even given the original premise (based on other comments) that it was supposed to be essentially for compute and storage, that’s a lot of hassle for incremental gains. Like, I’d love to get a 50% boost out of my cpu and a bunch of extra storage, but not if it means regular maintenance cycles of suppressing a transistor rebellion.
- clircle 3y agoBlast from the past! I actually used this Cookbook to look up a matrix derivative that I used in my PhD thesis!
- tnecniv 3y agoI used the derivatives section on basically every homework assignment in grad school. I wish CAS systems were better at linear algebra!
- hoosieree 3y agoI love the "Notation and Nomenclature" section. So many academic papers assume readers will infer the type of a variable by its font styling, which is frustrating if you aren't already very knowledgeable in that particular field. To clarify - using an actual programming language (any language, I'm not picky) would still be better than inventing an ad-hoc, unverifiable font-based type system every time you publish a new paper. But having a "Notation" section is still vastly better than the usual approach of "guess what I mean".
- hgsgm 3y agoMathematical notation is a programming language. The notation section is type definitions.
- BeetleB 3y ago> Mathematical notation is a programming language. It actually isn't - the notation has lots of ambiguities that don't confuse mathematicians because they are aware of the context. On Proof and Progress in Mathematics[1][2] is a great essay by a Field's medalist. Part of the essay discusses this very topic, and why mathematicians choose not to use a formal notation for every day work. Some quotes from it: > The standard of correctness and completeness necessary to get a computer program to work at all is a couple of orders of magnitude higher than the mathematical community’s standard of valid proofs. Nonetheless, large computer programs, even when they have been very carefully written and very carefully tested, always seem to have bugs. > When one considers how hard it is to write a computer program even approaching the intellectual scope of a good mathematical paper, and how much greater time and effort have to be put into it to make it “almost” formally correct, it is preposterous to claim that mathematics as we practice it is anywhere near formally correct. [1] https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236 [2] I discovered it via HN comments a while ago.
- 141205 3y agoYes, but I think this presents the core of the problem in modern pedagogical methods when it comes to mathematics. The Bourbaki attempted to reduce math to a highly axiomatic foundation, while disregarding the intuition and visualization that used to be a part of mathematics. The issue is that this sort of "code only" or "language only" approach really works when mathematics is a true "perfect language", the likes of which philosophers were attempting to construct, but is likely in fact impossible to create. Unfortunately, not only did the ideas of the Bourbaki fail, as modern research advances mostly still work with intuition instead of their ideas, but their approach polluted and ruined education. Many "textbooks" are terribly written reference books that have gaps and ambiguities that only people already knowledgeable in the field know about. Rudin's Analysis textbooks are probably the classical example of this. I would argue that any notation or abuse of notation is fine within insular fields and private practice, but there does need to be a leaning towards universal notation within all pedagogical works, at least up through all the core Algebra, Analysis, and Geometry and Topology work that you would see within a PHD qualifying exam.
- SpaceManNabs 3y agoNumerator vs Denominator layout. The great debate of matrix algebra.
- mbustamanter 3y agoThis cookbook was insightful in the sense that I once tried proving several of its identities via Kronecker products but then found that it was much easier using tensor notation, so easy that I almost forgot Kronecker products altogether. I put together some proofs in my blog [0] (note: it's incomplete and the URL might change!). [0] https://mbustamanter.github.io/ssg-blog/2022/matder1/ https://mbustamanter.github.io/ssg-blog/2022/matder1/
- jey 3y agoTom Minka's "Old and New Matrix Algebra Useful for Statistics" is also really handy: https://tminka.github.io/papers/matrix/minka-matrix.pdf https://tminka.github.io/papers/matrix/minka-matrix.pdf I used to always stare at these two PDFs while deriving machine learning algorithms back in the day. (At least my hand rolled code C++ still beats PyTorch's reverse autodiff performance.)
- dang 3y agoRelated: The Matrix Cookbook (2012) [pdf] - https://news.ycombinator.com/item?id=18566449 https://news.ycombinator.com/item?id=18566449 - Nov 2018 (39 comments) The Matrix Cookbook (2012) [pdf] - https://news.ycombinator.com/item?id=14726223 https://news.ycombinator.com/item?id=14726223 - July 2017 (9 comments)
- mock-possum 3y agohonestly pretty disappointed that this doesn't have Neo's famous Buckeyes recipe - even Morpheus's Enchilada Casserole or that juicy and delicious steak Cypher snacks on during his meeting with Smith would've been appreciated. Hell even Trinity's Ranchwater would be nice, even if it's only a couple ingredients, there's just something about the way she makes them.
- nomorepdfs 3y agoThis pattern emerging of people posting PDF downloads should be discouraged and discontinued. I dont need to explain that.