J. M.
Reputation
50,198
416/400 score
 Nov 23 comment Why does this matrix give the derivative of a function? In fact, this is sometimes taken to be the definition of a matrix function when evaluated at a Jordan block; see this. See this paper as well. Nov 21 revised The approximation of first-ordered modified Bessel function of the second kind edited tags Nov 19 revised Why does the google calculator give tan 90 degrees = 1.6331779e+16? edited tags Nov 16 comment proof: inverse of lower triangular identity matrix Your observation only works for so-called "Gauss transforms", which are rank-1 corrections to the identity matrix that turn up in LU decomposition. Golub and Van Loan should have a proof of this. Nov 14 awarded Enlightened Nov 14 awarded Nice Answer Nov 13 awarded Revival Nov 13 revised Associated Legendre polynomials of fractional order added 4 characters in body Nov 9 revised What is Cauchy Schwarz in 8th grade terms? added 2 characters in body Nov 8 comment Does the phrase “If you don't use it, you lose it” apply to mathematics? Not having a very good memory, I still forget things even if only a short span of time has passed since the last time I used it. However, I compensate by trying to at least remember where to look things up (i.e. references) whenever I need them. But yes, practice is key, as previously mentioned. Nov 7 revised pdfs of i.i.d. with uniform distribution deleted 1 character in body Nov 6 comment Can any 3d rotation be done with only two angles? Here's a different way of looking at it: recall that any 3D rotation matrix has an axis-angle representation (one angle). But, this axis is not necessarily aligned to the coordinate axes! So, you need one rotation to take the axis to a coordinate plane (two angles), and another one to have it coincide with a coordinate axis (three angles). Nov 4 comment What kind of distribution is this (PDF bounded within interval)? For reference: the PDF presented here can be seen as a suitably scaled quadratic B-spline basis function. Nov 4 comment pdfs of i.i.d. with uniform distribution Well, looking at the convolution-based recursive definition, I suddenly recalled that one way to start B-spline theory is to consider them as repeated convolutions of a boxcar function. Here are two references, among others. Nov 4 comment pdfs of i.i.d. with uniform distribution For comparison purposes: BSplineBasis[n - 1, x/n] // PiecewiseExpand // Simplify. It's amusing how a function from a distant field can represent the solution... Nov 3 accepted A golden ratio series from a comic book Nov 2 awarded Good Answer Nov 2 revised What does | mean? added 3 characters in body Nov 1 awarded eigenvalues-eigenvectors Oct 31 answered Eigenvectors and ''eigenrows''