Giulio R's user avatar
Giulio R's user avatar
Giulio R's user avatar
Giulio R
  • Member for 3 years, 9 months
  • Last seen this week
  • Lisbon
7 votes
Accepted

Let $f : M_n → C$ be a linear map. Show that there exists a matrix $B$ ∈ $M_n$ such that $f(A) = tr(BA)$, $∀ A ∈ M_n$

6 votes

Evaluating $\sum\limits_{n=0}^\infty\Gamma(in+1)$

6 votes

Evaluating a binomial sum involving $1/m^m$

5 votes
Accepted

Finding general formula for the sequence $b_{n+1} = 2\cdot b_n + 2^{n-1}$

5 votes

Combinatorics and set theory question

5 votes
Accepted

Computing the Integral $\int_0^{2\pi} \frac{1 + \sin(\theta)}{3 + \cos(\theta)}d \theta$

5 votes
Accepted

How to prove the inequality including Bessel functions?

5 votes
Accepted

Let $a_n$ be a sequence of nonnegative numbers such that $a_n \rightarrow b$. Then, $\lim_{n \rightarrow \infty} \frac{(a_{n+1})^{n+1}}{(a_n)^n}$ =?

4 votes

Interpreting Taylor series as exponentiating an operator

4 votes

If $\operatorname{rank}(A) = \operatorname{rank}(A^2)$, thn $\operatorname{rank}(A) = \operatorname{rank}(A^n)$, if $A$ has $2$ rows and $2$ columns?

4 votes
Accepted

Lie algebra of a closed subgroup

4 votes
Accepted

Simplifying the determinant of a matrix.

4 votes
Accepted

Showing $V(a) = \{ (z_1, ..., z_n) \in \mathbb{C}^n : \sum_{j=1}^{n}{|z_j|^2} = 1, \sum_{j=1}^{n}{z_j^{a_j}} = 0\}$ is a manifold.

4 votes
Accepted

A weaker condition of the definition of topology

4 votes
Accepted

How to solve this problem with Linear Algebra?

4 votes
Accepted

Is there a natural way to build a volume form on an oriented Poisson manifold?

4 votes

Compute integral $\int^\infty_{-\infty}\frac{1}{\big(\frac89x^2+\frac23\big)\sqrt{\frac{x^2}{3}+1}}~dx$

3 votes
Accepted

On combinatoric equality $\sum_{i=1}^{n-1}{n\choose i} i^{i-1} (n-i)^{n-i-1}=2(n-1)n^{n-2}$

3 votes
Accepted

A sequence derived from $\lceil \sin (2n) \rceil$ with some interesting features

3 votes

Interesting infinite product $\sqrt{2}-1=\dfrac{1\cdot7\cdot9\cdot15\cdot17\cdot23\cdots}{3\cdot5\cdot11\cdot13\cdot19\cdot21\cdots}$

3 votes
Accepted

Does this condition imply orthogonality?

3 votes

How to characterize homogenous functions?

3 votes
Accepted

Differentiability of Implicit Function

3 votes
Accepted

Lax pair for advection equation

3 votes
Accepted

Prove that U(n) is an embedded submanifold.

3 votes
Accepted

Closed form for $ a_n = 1-2^4 +3^4 - 4^4 + ... \pm (-1)^n \cdot n^4 $ using Generating Functions

2 votes
Accepted

Semisimple regular elements of the Lie algebra $\mathfrak{sl}_n(\mathbb{C})$

2 votes

Find all eigenvalues of $S, T$ and their corresponding algebraic multiplicities and geometric multiplicities.

2 votes

If exponentiation of a matrix is upper triangular show it is upper triangular itself

2 votes

Integral of a product of Legendre polynomials