Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 75

How to compare Dehn Invariants

I just learned about tensor products in the context of Hilbert's Third Problem. I think I understand what a tensor product is, at least what it was used for in...

Asked on 11/20/2021 by MandelBroccoli

0 answer

Can you find a single solution of this function?

While playing around with the fresnel integrals, I came across this tantalizing power series (it is actually a particular hypergeometric series) which looks really similar to cosine! I am...

Asked on 11/20/2021 by guavas222

1 answer

Definition of vertex in graph theory

What is the definition of vertex in graph theory?Is it just an endpoint of an edge.If we consider it like that then won't there be an uncountably many number...

Asked on 11/20/2021

1 answer

Gluing Construction of the Grassmanian in Eisenbud/Harris

On page 119 of Eisenbud and Harris' "The Geometry of Schemes," they construct the Grassmanian by gluing. We start by identifying $k$-dimensional subspaces of an $n$-dimensional space ...

Asked on 11/19/2021 by Johnny Apple

0 answer

general matrix determinant lemma

Starting from Prove $mathbf{det(I+xy^T+uv^T)}=(1+mathbf{y^Tx})(1+mathbf{v^Tu)-(x^Tv)(y^Tu)}$for example, is it possible to generalize as follows? If $w_i$, $1leq ileq n$ is a basis for $mathbb{R}^n$, is there a...

Asked on 11/19/2021 by Silbraz

1 answer

Pretty conjecture $x^{left(frac{y}{x}right)^n}+y^{left(frac{x}{y}right)^n}leq 1$

inspired (again) by an inequality of Vasile Cirtoaje I propose my own conjecture :Let $x,y>0$ such that $x+y=1$ and $ngeq 1$ a natural number then we have...

Asked on 11/19/2021

2 answer

What fragment of ZFC do we need to prove Zorn's lemma?

It is extremely well-known that Zorn's lemma is a theorem of ZFC. My interest is in a certain finitely-axiomatisable fragment of ZFC, sometimes called RZC (restricted Zermelo with choice) or...

Asked on 11/19/2021 by Zhen Lin

3 answer

Let$A$ be a $3times3$ real symmetric matrix such that $A^6=I$ . Then $A^2=I$

Let$A$ be a $3times3$ real symmetric matrix such $ A^6=I$ . Then $A^2=I$. How can I prove this statement is true or false? As it is...

Asked on 11/19/2021

2 answer

Heron's Formula Intuitive Geometric Proof

This is not the usual request for an intuitive proof, which has been asked already. Having looked at various sources, I've basically concluded that Heron's formula relies on proving...

Asked on 11/19/2021

1 answer

For a given circle, prove that the lines of intersections by circles that pass through two given points converge at one point.

The problem is from Kiselev's Geometry exercise 410:Given a circle O and two points A and B. Through these points, severalcircles are drawn such that each of them intersects...

Asked on 11/19/2021 by Taxxi

1 answer

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