Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 85

Prime ideals of $Bbb C[x, y]$

In the exercise 3.2.E of Vakil's "Foundations of Algebraic Geometry", it is asked to prove that all the prime ideals of $Bbb C[x, y]$ are of the form ...

Asked on 11/14/2021 by Nuntractatuses Amável

1 answer

Is a convex set of permutation matrices $ntimes n$ ($mathbb{P}_{n}cap mathbb{C}$) a singleton?

$mathbb{C}$ is a closed convex set. In detail, $min_{Xinmathbb{P}_{n}capmathbb{C}} f(x):= x^{T}Wx + c^{T}x$ $x:=vec(X)in mathbb{R}^{n^2}$ What is wrong if I remove the $capmathbb{C}$ as the below?...

Asked on 11/14/2021 by Joey Cho

0 answer

Let $0leq a leq b leq 1$. Then we have for all natural numbers $mgeq 2$ the inequality $b^{frac m2}-a^{frac m2} leqfrac m2(b-a)$

Let $0leq a leq b leq 1$. Then we have for all natural numbers $mgeq 2$ the inequality $b^{frac{m}{2}}-a^{frac{m}{2}} leqfrac{m}{2}left(b-aright)$. My first idea was to consider the...

Asked on 11/14/2021 by Giuliano Cantina

3 answer

Let $x=begin{bmatrix}3cr4end{bmatrix}$ and $A=begin{bmatrix}0&x^Tcr x&0end{bmatrix}$ is A diagonizable?

I had a problem: let $x=begin{bmatrix}3cr4end{bmatrix}$ and $A=begin{bmatrix}0&x^Tcr x&0end{bmatrix}$ is A diagonizable? But when I plug in the matrix x and its transpose into A the dimensions don't...

Asked on 11/14/2021

1 answer

Is a directed graph different from a flow graph?

I'm trying to understand directed graphs in a more applied way, especially in the context of the dataflow programming paradigm. Is the following flow chart a directed graph? ...

Asked on 11/14/2021

1 answer

The diophantine equation $ m = x^2 + 7y^2 $

I found this theorem.A prime number $m ne 7$ can be written as $x^2 + 7y^2$ for $x,y$ integersiff $m$ is one of these residues...

Asked on 11/14/2021 by peter.petrov

2 answer

Is there any visual representation on why (certain) trigonometric functions have infinite derivatives.

As far as I understand, the first derivative of a function gives you the slope at a particular point.The second derivative would give the concavity.The third derivative would...

Asked on 11/14/2021 by Teabx

2 answer

Is $(I circ A - I circ B)$ positive semi-definite if $A$, $B$ and $A - B$ are positive semi-definite?

Let $A$ and $B$ are positive definite and positive semi-definite matrices, respectively. $A - B$ is positive semi-definite.Is it true that $(I circ A - I...

Asked on 11/14/2021

1 answer

$f^{*}$ is surjective if and only if $f$ is injective

I’m having a hard time understanding this proof and I hope someone could help me.Theorem: Let $f: A rightarrow B$ a map. Think of this map as inducing the...

Asked on 11/14/2021 by Air Mike

2 answer

Rational singularity of Spec, Proj and Spec of localization of a standard graded $2$-dimensional ring

If $X$ is a two dimensional Noetherian reduced excellent scheme, then we know by a Theorem of Lipman that $X$ has a desingularization, i.e., there...

Asked on 11/14/2021

0 answer

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