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olivier dot begassat dot cours at gmail dot com


Feb
26
comment Maximal finite order of Abelian Groups
Your conclusion on $r,s,p,m$ is wrong.
Feb
26
answered Reference for Lie-algebra valued differential forms
Feb
26
answered Example of a group where $o(a)$ and $o(b)$ are finite but $o(ab)$ is infinite
Feb
26
comment Example of a group where $o(a)$ and $o(b)$ are finite but $o(ab)$ is infinite
I like this answer a lot!
Feb
26
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).
Feb
25
comment A certain element which makes functionals positive
Do you need clarification?
Feb
24
answered A certain element which makes functionals positive
Feb
24
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...
Feb
24
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 :)
Feb
24
comment Analysis and real analysis
This can be obtained as a corollary to the Stone-Weierstrass theorem. Are you familiar with this theorem?
Feb
24
answered Exercise 6.1 in Serre's Representations of Finite Groups
Feb
24
revised Why is a matrix of indeterminates diagonalizable?
added 38 characters in body
Feb
24
answered Why is a matrix of indeterminates diagonalizable?
Feb
22
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.
Feb
20
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.
Feb
19
revised Matrices and Linear Transformation
rolled back to a previous revision
Feb
18
comment Permutation question. $qpq^{-1}$, $q,p,r,s \in S_{8}$.
How did you fill in the numbers that are not question marks?
Feb
18
comment Counting points in $\mathbb{F}_{p^n}$
I guess you could count using a generator of the cyclic group $\Bbb F_{p^n}^{\times}$.
Feb
14
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!
Feb
14
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 $\Bbb F_4$?