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Aug
6
revised Can the “generalized commutator bracket” $[(a,b,c)]$ be written using only the usual commutator bracket and $\mathbb{Q}$-linear combinations?
added 337 characters in body
Aug
6
answered Can the “generalized commutator bracket” $[(a,b,c)]$ be written using only the usual commutator bracket and $\mathbb{Q}$-linear combinations?
Aug
4
comment Solve the trig equation $\cos\theta − \sin\theta = 1$
@TheNewGuy : Yes, exactly !
Aug
4
comment Solve the trig equation $\cos\theta − \sin\theta = 1$
If you square everything you may potentially get some extra solutions (solutions of $\cos \theta - \sin \theta = -1$) but can get rid of it after if that happens.
Aug
2
comment How to find $p\in \Bbb C[X]$ given $p(p(X))$
There might be several $p$ leading to the same $p(p(X))$. For example $p = X$, and $p = a-X$ (for any $a \in \mathbb{C}$) lead to the same polynomial $p \circ p$.
Aug
1
comment Is it possible to find a companion matrix of a polynomial which is also hermitian?
@sintetico : Yes this is what I claim, at least if my proof is correct :)
Aug
1
revised Is it possible to find a companion matrix of a polynomial which is also hermitian?
added 7 characters in body
Aug
1
comment Is it possible to find a companion matrix of a polynomial which is also hermitian?
@sintetico : I think it does answer at least partly. I've inserted an explanation as to why if such a "rational companion matrix" were Hermitian for hyperbolic polynomials, it should also be hermitian for all real polynomials (which is impossible from the first observation). I'm sorry, but it's rather a result of non existence...
Aug
1
revised Is it possible to find a companion matrix of a polynomial which is also hermitian?
added 433 characters in body
Aug
1
comment Generalized limit of $\left(1+\frac{f(n)}{n}\right)^n$
@dimebucker91 : You're welcome :) I think what you wrote is correct, indeed $\lim_{n \to \infty} f(n)$, however complicated, is just a number after all.
Aug
1
answered Generalized limit of $\left(1+\frac{f(n)}{n}\right)^n$
Aug
1
revised Is it possible to find a companion matrix of a polynomial which is also hermitian?
added 2544 characters in body
Jul
31
answered Is it possible to find a companion matrix of a polynomial which is also hermitian?
Jul
19
comment Question about $C_0(X)$ is unital iff X is compact
@NateEldredge: You're right, sorry !
Jul
19
comment Question about $C_0(X)$ is unital iff X is compact
Recall $C_0(X)$ is the space of continuous compactly supported functions. Since $1_X$ is continuous, it is in $C_0(X)$ iff it is compactly supported, iff $X$ itself is compact.
Jul
19
comment If the square of a number is even, then the number if even. Isn't that not true for 2?
To be more precise one should say "if the square of an integer is even, then that integer is even". When writing $n^2$ it is implied $n$ is an integer, so $2$ is not the square in that sense.
Jul
11
comment Alternating sum of product of Fibonacci numbers
Using the formula for $F_n$ as a linear combination of geometric sequences, I think you should get an expression of your sum as a linear combination of geometric sums.
Jul
10
comment Find an equivalent of this function,
First try solving (a) when $f = 1$ is just the constant function equal to $1$. Then, when $f$ is arbitrary, only what happens around $0$ will play a role in the equivalent (this is the part that blows up).
Jul
10
answered Congruence of 2 fractions—how to properly rewrite in terms without modulo?
Jul
8
answered Real part of $\frac{1-e^{(n+1)i\theta}}{1-e^{i\theta}}$