4,382 reputation
1636
bio website
location Besançon, France
age 34
visits member for 1 year, 11 months
seen 16 mins ago

Mathematics is a hobby for me, and MSE helps me not to forget too much what I learned in university (MS in applied mathematics at Lyon 1). I like especially real and complex analysis, trigonometry, numerical analysis, finite groups theory, number theory and combinatorics. I am not allergic to other fields.

Contact: arbautjc at gmail dot com


3h
comment Permutation matrices
Hint: write the product on an example, with the usual setting ($A$ on the left of product $AB$, $B$ on top of it), to help visualize. A $4\times4$ example should be enough to understand.
13h
comment Self-learning mathematics - help needed!
For the 1.: fight the temptation. "Basics", or better "foundations", are much more difficult than the average mathematical subject. You must understand basics up to some point (say, Halmos' Naive set theory), but it's useless to go much deeper than that, unless you want to specialize on this.
13h
comment Leading eigenvalues of large sparse unsymmetric matrix
caam.rice.edu/software/ARPACK and the forked github.com/opencollab/arpack-ng
13h
comment Runge's Phenomenon
If you want to play with approximations by high degree polynomials, there is a nice book coming with a Matlab software library: Approximation Theory and Approximation Practice, by Lloyd Trefethen. The software package is chebfun, dealing with interpolation by polynomials in Chebyshev basis.
13h
comment Modifying U=mxn SVD Algorithm to U=mxm Algorithm
@IanMallett Since there are plenty of implementations, you can either use a library (I don't see why you can't, but I don't know your constraints), either extract the important source code and integrate it in your system. There are good implementations in C (for example from gsl), Fortran (for example from Lapack), and probably C++ as well. So I don't really see the problem. Usually, the simple way to go is just to find a Lapack compiled for your OS/compiler, and integrate it, within any language (even Excel's VBA).
18h
comment Time series library in Java
Maybe this, but it looks oldish, as well as this. Weka is more recent, but I don't know if it will fit your needs.
18h
comment Time series library in Java
By math3, do you refer to Apache Commons Math?
19h
comment Abstract Algebra Book Request
Maybe this? amazon.com/Galois-Theory-Graduate-Texts-Mathematics/dp/… Even though it's in the "Graduate Texts in Mathematics" collection (so maybe too high level), it introduces Galois theory using similar approach as Galois himself, so ok for the historical perspective.
19h
comment Solve the function from the composition
@sdg Out of curiosity, which website?
19h
comment Solve the function from the composition
On what set is it supposed to be true?
21h
comment Find $\int_{-1}^1 (8x^3 + 14x^2 + 6x + 3)dx$.
In the last steps, it's not $+9$, but $+6$.
21h
comment Showing that a Unit Speed Curve is a Circle.
Even if you show the points of your curve lie on a circle, you still have to prove they describe the whole circle. It looks obvious, but you may also have a curve describing only half a circle, for example. You can find an orthogonal linear transformation in space that transform your curve in the parametric equation of a circle in an easy plane like xOy.
2d
comment Simplifying/solving a logarithm $\log_24^{2n}$
@user1729 Ok, I must admit, when I saw this answer in the review list, I didn't check the question :-)
2d
comment Simplifying/solving a logarithm $\log_24^{2n}$
@user1729 It's not an answer, in the sense that it should be a comment. You don't need a full answer to say "yes".
2d
comment Simplifying/solving a logarithm $\log_24^{2n}$
This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post - you can always comment on your own posts, and once you have sufficient reputation you will be able to comment on any post.
2d
comment Direct evaluation of a series from Euler's identity.
Depends on how you define $\pi$, but it can be a direct consequence of a definition: "$\pi/2$ is the smallest positive root of the series $\sum_{k=0}^{\infty} (-1)^k\frac{x^{2k}}{(2k)!}$", plus addition (or duplication) formula, that can be proved with Cauchy product of series.
2d
comment Collision of 8 Digit, Base-36 Numbers
With $n=36^8$, you can rewrite the fraction as $$\frac{n}{n}\cdot\frac{n-1}{n}\cdots\frac{n-9999}{n}\cdot$$ With this and Maxima, I find that your probability is $$1.77215913956941117517... \cdot 10^{-5}$$
2d
comment Simple linear regression seems off
Don't forget distances are measuredvertically. Maybe you should consider regression of $x$ with regressor $y$, or regression with minimal euclidian distance (it's like a principal component analysis with 1 axis).
2d
comment If $f$ is injective and $g$ is surjective, is $g\circ f$ bijective?
To answer the question in title: no, but the converse is true. A simple counterexample, $g:\Bbb R\rightarrow \Bbb R^+$ and $f:\Bbb R \rightarrow \Bbb R$, with $f(x)=x$ and $g(x)=x^2$.
2d
comment Fields - Proof that every multiple of zero equals zero
Simpler: $0a=(0+0)a=0a+0a$, thus by adding $-(0a)$ on both left and right, $0a=0$.