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Closed form solution for $XAX^{T}=B$

Let $d times d$ matrices $A, B$ be positive definite. Is there a closed form solution for the following quadratic equation in $X$? $$X A X^{T}...

Asked on 11/03/2021

1 answer

Specific notions of forcing from the point of view of category theory

I'm trying to learn about the topos of sheaves and the double negation topology to try to go through the independence of CH from a categorical perspective. I'm curious in...

Asked on 11/03/2021 by Rachid Atmai

1 answer

Most memorable titles

Given the vast number of new papers / preprints that hit the internet everyday, one factor that may help papers stand out for a broader, though possibly more casual, audience...

Asked on 11/03/2021 by Suvrit

122 answer

Abelian subgroup in an infinite non-abelian 3-group

Does an infinite non-abelian 3-group of exponent greater than or equal to 9 have an infinite abelian subgroup? I know that every 2-group or 3-group of exponent 3 has an...

Asked on 11/03/2021 by D. N.

1 answer

Is $x^p-x+1$ always irreducible in $mathbb F_p[x]$?

It seems that for any prime number $p$ and for any non-zero element $a$ in the finite field $mathbb F_p$, the polynomial $x^p-x+a$ is irreducible over $mathbb F_p$. (It is...

Asked on 11/03/2021 by Roland Bacher

5 answer

Weinstein neighborhood theorem for Lagrangians with Legendrian boundary

$require{AMScd}$ Weinstein's neighborhood theorem says that every Lagrangian has a standard neighborhood. The more precise statement goes like this.Theorem 1: (Lagrangian Neighborhood Theorem) Let $(X,omega)$ be a symplectic...

Asked on 11/03/2021 by Julian Chaidez

1 answer

Surmounting set-theoretical difficulties in algebraic geometry

The category $text{AffSch}_S$ of affine schemes over some base affine scheme $S$ is not essentially small. This lends itself to certain set-theoretical difficulties when working with a category...

Asked on 11/03/2021 by leibnewtz

1 answer

Need help in understanding meaning of a notation and theorem used in research paper due to a reference being in German Language

I thought of utilizing this lockdown period to study research papers in number theory by myself. I began reading the research paper By T Estermann ->" On Goldbach Problem...

Asked on 11/03/2021

2 answer

Examples of improved notation that impacted research?

The intention of this question is to find practical examples of improved mathematical notation that enabled actual progress in someone's research work. I am aware that there is a related...

Asked on 11/03/2021

7 answer

From Zurab's integral representation for the Apéry's constant to almost impossible integrals

I would like to know if the following integrals are known, or in case that aren't in the literature we can calculate these in closed-form (in terms of elementary and...

Asked on 11/03/2021

2 answer

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