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Apr
25
comment Construct certain univariate functions over bounded interval having given set of moments
This seems more like a math question than a Mathematica question.
Apr
25
revised Why is this determinant positive?
added 9 characters in body
Apr
24
comment Are we allowed to compare infinities?
The drawing should sell it, hopefully. :)
Apr
24
comment Are we allowed to compare infinities?
...with attribution, of course.
Apr
24
comment Why is Euler's number used as a base for logarithms?
Your last formula is exactly what was being said in your quote, but couched in admittedly very high-level language.
Apr
23
comment Why is Euler's number used as a base for logarithms?
"Isn't it much simpler to use 10 as a base?" - it depends on the application, of course. For things like pH and other p-values, of course the common logarithm is the convenient one. For calculus, due to the property peter mentioned (among many other things), $e$ is the "nice" base.
Apr
22
comment Showing that a matrix is symmetric positive definite
You can easily reformulate the route here in terms of LU; the only important facts are that SPD matrices do not need pivoting, and there is a relationship between LU and both Cholesky and $\mathbf L\mathbf D\mathbf L^\top$.
Apr
22
comment Showing that a matrix is symmetric positive definite
…and you never covered Schur complements either?
Apr
21
answered Showing that a matrix is symmetric positive definite
Apr
20
comment What equation produces this curve?
Certainly, the basis changes between the Hermite and Bézier systems are well-known to those who know them. :) In any case, sigmoids such as the OP's are very cheaply constructed as appropriate interpolating polynomials with prescribed derivatives, and your procedure is the most straightforward way to go about it. As another aside: computer graphics buffs may be more familiar with this as (an appropriate rescaling of) the smoothstep() function.
Apr
20
comment What equation produces this curve?
For searching purposes: what was constructed here is a cubic Hermite interpolating polynomial. Usually does a nice job if the derivative values are sanely chosen.
Apr
14
revised What happens if I repeatedly alternately normalize the rows and columns of a matrix?
edited tags
Apr
13
comment Is basis change ever useful in practical linear algebra?
Not just for powers; in fact, this can be used anytime one wants to evaluate a function with matrix arguments, like the exponential or the sine. In the nondiagonalizable case, one has to be content with the Jordan form.
Apr
11
revised Efficiently evaluating $\int x^{4}e^{-x}dx$
edited title
Apr
10
revised Is the catenary the trajectory of anything?
deleted 2 characters in body
Apr
10
comment Is the catenary the trajectory of anything?
@Oscar, yes, the Hall/Wagon paper also addresses the infinite-sides case, too. :)
Apr
10
comment Improper integral involving sinc function and Pochhammer symbol
A few manipulations give the equivalent integral $$\int_{-\infty}^\infty \frac{\Gamma(1+n)}{\Gamma(1+t)\Gamma(1-t+n)}\mathrm dt=\int_{-\infty}^\infty \binom{n}{t}\mathrm dt$$
Apr
10
comment What's problematic about finding out if a large number is Prime or not?
It is hard to check for a large number's primality, yes, but at least that is a comparatively easier task than attempting to factor a large number. (As an aside, most of the efficient probabilistic tests should be properly called "compositeness tests", since they can show compositeness with certainty, but not primality.)
Apr
10
comment Function that maps the “pureness” of a rational number?
Put another way, your "another possibility" is just the ratio of the LCM to the GCD.
Apr
10
comment Computing Bezier curve of a high order
...depends on the configuration of the ten points of course. OP unfortunately did not show even a picture.