50,119 reputation
339101
bio website www-math.univ-poitiers.fr/…
location Poitiers, France
age 54
visits member for 3 years
seen 8 hours ago

professor of mathematics at the Université de Poitiers (France)


8h
revised Olympic elementary combinatorics problem
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8h
comment Is there a topological proof that additon and multiplication are continous functions from $\mathbb R \times \mathbb R $ into $\mathbb R $?
It is not clear what you are asking. For me the definition of continuous function is topological, and proving something is continuous will ultimately have to use the definition somewhere. So I would say every proof meets your criteria.
8h
revised How to show that an ideal of $F[x]$ containing an irreducible polynomial of degree $n$ and a nonzero polynomial of degree $<n$ is $F[x]$?
edited tags; edited title
8h
answered How to show that an ideal of $F[x]$ containing an irreducible polynomial of degree $n$ and a nonzero polynomial of degree $<n$ is $F[x]$?
8h
revised How to show that an ideal of $F[x]$ containing an irreducible polynomial of degree $n$ and a nonzero polynomial of degree $<n$ is $F[x]$?
Make title ask for the same thing as the question body.
9h
answered Olympic elementary combinatorics problem
10h
revised Commutation when minimal and characteristic polynomial agree
added 100 characters in body
10h
answered Commutation when minimal and characteristic polynomial agree
12h
answered 3x3 matrices completely determined by their characteristic and minimal polynomials
13h
revised Prove similarity of matrices with the same characteristic and same minimal polynomials
less confusing title; it could be read charpoly=minpoly, which is not the case
14h
revised Minimal polynomials and cyclic subspaces
clean up editing mess at end of first paragraph
17h
comment Proving that elementary row operations are preserved after multiplication
Also your title does not really correspond to what you seem to be actually asking (and in fact does not seem to make much sense at all). There is nothing in particular "preserved" here.
17h
comment Proving that elementary row operations are preserved after multiplication
If you want, you can use these formulations to define what change an elementary row respectively column operation realises. Then there is nothing to prove.
17h
comment Proof of Vector Space Axioms
You can (and should) verify that the axioms hold in particular cases, so that you are justified in calling those cases vector spaces. But indeed in the abstract theory, one just assumes that whenever one talks about a vector space, the axioms hold.
17h
comment If $A\times B \subset A\times C$, does it follow that $B \subset C$?
The way the question is phrased, it seems to me that they want most of all to want to hear "no", namely that students be aware that sets can be empty. Of course your answer is more complete than that.
17h
revised Minimal polynomials and cyclic subspaces
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18h
comment If $A\times B \subset A\times C$, does it follow that $B \subset C$?
If you must add a hypothesis, then you have not answered the given question. So you should say: "The answer is no. However, if you add a hypothesis... ".
1d
comment Minimal polynomials and cyclic subspaces
I think the "canonical" proof is to use the Rational Canonical Form, which works over any field, and immediately gives the the result (see the link in my answer). I've tried to give a more direct argument as well though.
1d
comment Minimal polynomials and cyclic subspaces
I don't think that it is easier to prove that all transformations with equal characteristic and minimal polynomial $p(t)$ are similar than that it is to prove they are cyclic; in other words I think I would by similarity by proving both are cyclic.
1d
revised Minimal polynomials and cyclic subspaces
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