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Studying linear algebra rn and it's too freaky for me 😭
There's too much magickery, like you define a thing a certain way and suddenly it has 3 billion useful properties
I feel like calculus had carefully constructed definitions to specifically get the properties and uses you wanted but this is something completely different
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Linear Algebra proofs are ragebait, fym prove that a set of m mutually orthogonal, non-0 vectors can’t exist in R^n with m > n…like yeah no shit it won’t exist just think about it for two seconds 😭
Trade secrets mathematicians don't want you to know: it's all actually just linear algebra
Today in "math things that probably should have clicked for me sooner but I'm just happy they clicked": Gram-Schmidt is usually presented as "any finite-dimensional inner product space has an orthonormal basis", which is obviously very neat and useful to know. However, if you think about it, this also means that every single inner product (on a finite-dimensional vector space) is just the regular Euclidean dot product applied to a different basis! Which is, like, even cooler! "How do we formally explain why the Euclidean inner product is the 'correct' choice of a canonical inner product that matches our geometric intuition" is a question that's been stewing in my brain for a while, and now I have another good answer! :D
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my first gf was GF(2)
theyre selling WHAT on ebay now
When you're really short and sitting in the 3rd row in advanced linear algebra:
