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#math
<thermoplyae> The chain rule is so nice in matrix calculus
<thermoplyae> That makes up for any other injustices
<joblot> thermoplyae: you mean that it works at all, or that it has to be written backwards?
<thermoplyae> It has to be written backwards?
<joblot> thermoplyae: are gradients rows or columns?
<thermoplyae> I think I'm talking about vector calculus in terms of matrices and you're talking about something else
<thermoplyae> But, as far as I'm concerned, columns, I think
<theZero> hi -- how can i mathematically turn a number like this 567234 into 234567 (effectively moving the first three digits to the end, and last three to the front) ?
<yell0w> theZero, 567234 -1 -1 -1 -1 -1 ...... = 234567 ?
<yell0w> =))
<moqq> theZero: y=floor(x/1000)+1000*(x mod 1000)
<theZero> ok -- thx, i'll try that
<joblot> thermoplyae: well I think I'm just saying interchanging rows and columns also interchanges the order of AB vs BA
<joblot> A^T B^T = (BA)^T
<joblot> which means in one representation C = AB, whileas in the other C = BA
<joblot> which is trivial and not worth worrying about
<theZero> moqq: you're awesome!
<slava> i feel like a fool asking this, but now do i go from the reduced row echelon form to a basis for the null space?
<medfly> i feel like a fool not understanding what you just said, dont feel bad :-)
<joblot> slava: the reduced row echelon is a basis for the non-null basis
<seb-_> medfly: heh
<slava> joblot: the non-zero rows form a basis for the orthogonal complement of the kernel?
<seb-_> How can a mortal man defeat the Kraken?
<Kampen> harpoons?
<joblot> slava: yes
<slava> joblot: so how do i go from that to a basis of the kernel? i'm trying to write a program that does this
<joblot> slava: well computing the basis is easy (SV decomposition almost always works), so how do you compute the complement of this basis (r<n)?
<slava> i already have code to put the matrix in row echelon form. i'm not sure SVD is appropriate here because i want to keep everything as arbitrary precision rationals
<slava> you have to forgive my ignorance, its been four years since i last did anything with computational linear algebra
<slava> i could use gram-schmidt
<slava> or maybe not, because the basis for the complement is not necessarily orthonormal
<joblot> slava: if you are using arbitrary precision, then gram schmidt has no numerical problems
<joblot> slava: the basic thing is to compute the basis for the spanned space, then use something like GramSchmidt to compute the (necessarily orthoginal) vectors of the null space
<moqq> theZero: no prob
<keithnn2> slava, whats it for?
<slava> its also embarrassing to say that, because its so much more advanced than basic linear algebra, and really underscores that i should know basic linear algebra by now
<slava> i'm computing cohomology of lie algebras
<slava> right now i only have the betti numbers (rank - nullity) but i want a basis for the cohomology too
<slava> see, there's that joke about the math guy who's so far off the deep end that he can't use a calculator, and that's me :)
<keithnn2> well, math aint about numbers :)
<joblot> slava: those of us who haven't thought about lie algebras, or even relativity, for many (I mean many) years, must immediately recuse ourselves
<B33B5> hi all, I have been working on a problem and have got it down to the expression arctan(7/x)-arctan(5/x)
<B33B5> I was wondering if you can get it down further using any sort of compund angle formula or other trickery
<joblot> B33B5: atan a + atan b = atan [( a+b ) / 1 - ab]
<futurist> anyone know why a language has countably many closed terms?
<futurist> suppose it has countably many constants, and, for each n in N, countably many n-place functions
<futurist> i don't see how to do the listing
<Olathe> Isn't that like the rationals ?
<futurist> i don't see any way to encode a closed term as an ordered pair...
<futurist> you can have stuff like h(f(a,b), g(c,d,e))
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