# All Questions

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### Spectral graph theory: Interpretability of eigenvalues and -vectors

I thought "Wow!" when I learned that the eigenvector of the adjacency matrix of a cycle graph $C_n$ corresponding to the second largest eigenvalue gives the coordinates of the vertices when equally ...
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### why isn't the mobius band an algebraic line bundle?

When I hear the phrase "line bundle" the first thing that pops into my head is a mobius band. But this is a bad picture from an algebraic point of view since any line bundle on an affine variety is ...
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### What are the reasons for considering rings without identity?

I think a major reason is because Lie algebras don't have an identity, but I'm not really sure.
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### Why is the Gamma function shifted from the factorial by 1?

I've asked this question in every math class where the teacher has introduced the Gamma function, and never gotten a satisfactory answer. Not only does it seem more natural to extend the factorial ...
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### How do you axiomatize topology via nets?

Let $X$ be a set and let ${\mathcal N}$ be a collection of nets on $X.$ I've been told by several different people that ${\mathcal N}$ is the collection of convergent nets on $X$ with respect to some ...
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### Conditions for “bootstrapping” a smooth DM stack?

In the preprint "Smooth toric DM stacks", Fantechi, Mann and Nironi define the stacks of their title, and show that each of these can be obtained through the following sequence of steps: 1) start ...
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### A linear operator on $M_{n}(\mathbb{R})$ [on hold]

In this question $O(n)$ is the orthonormal group which is equpied with a unique Haar meaure. We define a linear map $T$ on $M_{n}(\mathbb{R})$ with $$T(A)=\int_{O(n)} (g^{-1}Ag)dg$$ What is the ...
### A reasonable framework to study properties of operator $A \mapsto KAK$ on Banach space
Let $K$ be a continuous linear operator on $C[0,1]$ (more, precisely, it is a linear integral operator). Then $K$ defines a continous linear operator $\widehat K$ on $\mathcal L(C[0,1])$ by the rule ...