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This problem arises from control theory, but it is actually a linear algebra problem. Static Output Feedback Stabilization Problem: Given the matrices $A \in \mathbb{R}^{n \times n}$, $B \in \mathbb{R}^{n \times m}$ and $C \in \mathbb{R}^{p \times n}$ is there exist a matrix $K \in \mathbb{R}^{m \times p}$ such that real part of all eigenvalues of the matrix ...


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One of the biggest questions is one of the simplest to understand: what is the lowest bound for the operation count of matrix-matrix multiplication? Or, in other words, Given two $n\times n$ matrices, what is the lowest bound of the exponent in the computational complexity of their product? The conjecture could be made more bold: Does there exist ...


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The question for the existence of a vector space analog of the Fano plane is open for any prime power value of $q$: Is there a set of $3$-dimensional subspaces of $\operatorname{GF}(q)^7$ such that every $2$-dimensional subspace is covered exactly once?


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Too long for a comment. You are needing $n$ such that there is an integer $k$ with, roughly: $$(2k+1)\pi- 2\epsilon_n < 2n < (2k+1)\pi$$ with $\epsilon_n =\arctan\frac{1}{n}$. Dividing by $2(2k+1)$, that means we need a $n$ so that: $$\frac{\pi}2 - \frac{\epsilon_n}{(2k+1)}<\frac{n}{2k+1} < \frac{\pi}2$$ So if we are seeking odd convergents ...


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Hmm, I think the requirements you impose on a possible answer are contradictory in some sense. Therefore I'd suggest to first take a look at the Unanswered Questions list in MSE itself.Where questions without a satisfactory answer go unnoticed, of course. Here is a short list of my personal favorites; I can't and I won't speak for the masses. When do ...


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These (and those of the form $n!-1$) are called factorial primes. We don't know if there are infinitely many. As pointed out by others, the polynomial $x$ works. More generally, $ax + b$ works when $a$ and $b$ are coprime; this follows from Dirichlet's theorem. For polynomials of degree at least two, not much is known. Even $x^2 + 1$ is a mystery. ...



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