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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
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Nov
19
revised Why does the google calculator give tan 90 degrees = 1.6331779e+16?
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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
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Nov
9
revised What is Cauchy Schwarz in 8th grade terms?
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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
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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?
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Nov
1
awarded  eigenvalues-eigenvectors
Oct
31
answered Eigenvectors and ''eigenrows''