Reputation
4,852
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
13 27
Newest
 Yearling
Impact
~52k people reached

5h
comment Solve the trig equation $\cos\theta − \sin\theta = 1$
@TheNewGuy : Yes, exactly !
5h
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.
2d
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 $\frac{1-e^{(n+1)i\theta}}{1-e^{i\theta}}$
Jun
26
comment $p$ and $r$ are primes greater than $2$. $p+r$ vs $p+2r$, which could be a prime number?
You need to find a divisor for $p+r$. Look at your example. What is the smallest (non trivial) divisor of $3+5$ ?
Jun
24
comment How do I derive $n!$ from this series?
Are you sure about that statement (it seems false) ? Where is it from ? Maybe give a bit more context.