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V.S.e.H.
  • Member for 7 years, 1 month
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16 votes
7 answers
1k views

Prove $ \frac{x_1-x_2}{x_n+x_1} + \frac{x_2-x_3}{x_1+x_2}+\cdots+ \frac{x_n-x_1}{x_{n-1} +x_n}\le 0$ s.t. $x_1+\cdots+x_n=1$

5 votes
2 answers
129 views

Prove $\sum_{k=1}^{n-1}\frac{(n-k)^2}{2k} \geq \frac{n^2\log(n)}{8}$

4 votes
1 answer
271 views

Prove that $\sum_{i,j=1}^n \frac{a_ia_j}{1 - a_i^2a_j^2}\geq 0$ where each $|a_i| < 1$

3 votes
1 answer
159 views

Does $f(t)+sf\left(\frac{r-t}{s}\right)$ have local extrema at $r/(s+1)$ and $-r/(s-1)$ for $s > 1$, $r \neq 0$.

3 votes
1 answer
568 views

Prove $x^2y + y^2z + z^2x \leq 4/27$, where $x+y+z=1, x\geq 0, y\geq 0, z\geq 0$ [duplicate]

3 votes
0 answers
121 views

Hall's marriage theorem: sufficiency proof by contraposition

3 votes
1 answer
88 views

Product of power means inequality: prove $M_0^{\frac{n}{n+k}}M_k^{\frac{k}{n+k}} \leq M_1$

2 votes
1 answer
265 views

If $A$ has distinct eigenvalues, then all matrices close enough to $A$ also have distinct eigenvalues

2 votes
1 answer
73 views

If $A\overline{A}$ is normal, then $A\overline{A}, \overline{A^*A}, AA^*$ commute.

1 vote
1 answer
59 views

If $A\in M_n$ is normal, $A = [A_{ij}]_{i,j=1}^k$, and the eigenvalues of $A$ are those of $A_{ii}\in M_{n_i}$, then $A_{ij}=0,i\neq j$

1 vote
0 answers
39 views

Show that the diagonal entries of a unitarily similar matrix are nonzero.

1 vote
0 answers
54 views

Let $U,V\in M_n$ be unitary, then there are unitary $X,Y,D\in M_n$, with $D$ diagonal, s.t. $U = XDY, V= Y^*DX^*$.

1 vote
0 answers
39 views

If $P_\mathcal{M} - P_\mathcal{N}$ is nonsingular, then $\mathcal{M}\oplus \mathcal{N}=\mathbb{R}^n$.

1 vote
0 answers
92 views

Convergence of the product of a sequence of specific family of matrices with exponential decay

1 vote
1 answer
34 views

$\theta''(x) \geq \rho > 0$ implies $\biggl|\int_a^be^{i\theta(x)}dx\biggr|\leq \frac{8}{\sqrt{\rho}}$

1 vote
0 answers
112 views

About the maximum distance between a point on a trajectory of a dynamical system, and its projection onto its linear interpolation

1 vote
0 answers
268 views

Is the transpose of a matrix exponential with itself positive semi-definite under certain conditions

1 vote
1 answer
62 views

Change of basis question from an exercise about finite Banach spaces and their duals

1 vote
1 answer
155 views

Radius of largest inscribed ball in unit simplex: how to formulate as optimization problem

1 vote
2 answers
200 views

Prove or disprove that if $f(t) = \frac{1}{e^{-nt}+n-1}$ and $x_1+\cdots+x_n=0$ then $\sum_{i=1}^n f(x_i)\leq 1$. [duplicate]

1 vote
0 answers
25 views

Minimum volume bounding box, subject to dynamics constraints

0 votes
1 answer
457 views

Computing the length and centroid of a parametric, vector-valued curve that involves a matrix exponential

0 votes
1 answer
80 views

$L^1$ norm minimization with a functional constraint

0 votes
0 answers
165 views

(LP problem) Find an optimal plane that contains a set of points in its positive half-space, such that it does not coincide with another plane

0 votes
1 answer
92 views

Core-nilpotent decomposition of $A-\lambda I$ where $\lambda$ is a simple eigenvalue of $A$