# Olivier Bégassat

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olivier dot begassat dot cours at gmail dot com

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 Feb26 comment Maximal finite order of Abelian Groups Your conclusion on $r,s,p,m$ is wrong. Feb26 answered Reference for Lie-algebra valued differential forms Feb26 answered Example of a group where $o(a)$ and $o(b)$ are finite but $o(ab)$ is infinite Feb26 comment Example of a group where $o(a)$ and $o(b)$ are finite but $o(ab)$ is infinite I like this answer a lot! Feb26 comment Showing $f_n(x) = \sin(nx)$ is not uniformly convergent on $[0,1]$ that's enough! if a sequence of functions converges uniformly to some function $f$, then it converges simply to that same function (that is pointwise). Feb25 comment A certain element which makes functionals positive Do you need clarification? Feb24 answered A certain element which makes functionals positive Feb24 comment A certain element which makes functionals positive You would have to add some extra hypothesis so as to exclude $f_0=-f_1$ for instance... Feb24 comment Reducibility of $P(X^2)$ sorry Hagen, it seems I accidentally down-voted your answer the first time around! Sorry about that, I undid the down-vote, and voted you up :) Feb24 comment Analysis and real analysis This can be obtained as a corollary to the Stone-Weierstrass theorem. Are you familiar with this theorem? Feb24 answered Exercise 6.1 in Serre's Representations of Finite Groups Feb24 revised Why is a matrix of indeterminates diagonalizable? added 38 characters in body Feb24 answered Why is a matrix of indeterminates diagonalizable? Feb22 comment homeomorphism between the real projective line and a circle The circle is given the subspace topology from the plane, and the projective line is given the quotient topology. Feb20 comment Purpose of Simultaneous Diagonalization A couple of applications come to mind: simultaneous diagonalisation allows to define the root space decomposition in a semi-simple Lie algebra. While not completely the same as simultaneous diagonalisation of endomorphisms, the spectral theorem in finite dimension says that any quadratic form shares a common orthogonal basis with a definite positive quadratic form. Furthermore, it can be a tool in proving certain results, such as the fact that any definite positive endomorphism of a finite dimensional euclidean space admits a unique definite positive square root. Feb19 revised Matrices and Linear Transformation rolled back to a previous revision Feb18 comment Permutation question. $qpq^{-1}$, $q,p,r,s \in S_{8}$. How did you fill in the numbers that are not question marks? Feb18 comment Counting points in $\mathbb{F}_{p^n}$ I guess you could count using a generator of the cyclic group $\Bbb F_{p^n}^{\times}$. Feb14 comment Size of conjugacy classes in $GL(4,2)$ So to you $GL(n^2,q)$ stands for the general linear group of an $n$ dimensional vector space over $\Bbb F_q$? In that case, I think you should clarify this in your question, because your notation isn't standard and has mislead @DerekHolt and myself. Also, this greatly simplifies the task of finding the conjugacy classes! Feb14 comment Size of conjugacy classes in $GL(4,2)$ Just to clarify, is $GL(4,2)$ the general linear group of a 4-dimensional vector space over $\Bbb F_2$, or the general linear group of a 2-dimensional vector space on $\Bbb F_4$?