Talk:Hessenberg variety

Typoes

There are some typos here that an expert should have no difficulty rectifying, but as a non-expert they threw me, to the extent that I'm reluctant to make changes myself in case I've misunderstood the intention.

The definition of a flag on the flag variety page is an increasing sequence of subspaces, so the explanation of $F_{(h(i))}$ in terms of the first $h(i)$ vectors in $F_{\bullet }$ is offputting. Is what is meant simply $F_{h(i)}$ , the $h(i)$ -th term in the sequence $F_{\bullet }$ ?
In the defining equation of ${\mathcal {H}}$ , presumably the $h_{i}$ should be $h(i)$ , and $\subset$ should be $\subseteq$ .
In the defining inequality for $h(i+1)$ , should $\max(i,h(i))$ perhaps be $\max(i+1,h(i))$ ?

Thanks! Andrewbt (talk) 05:48, 28 August 2013 (UTC)[reply]

Relation to Hessenberg matrix?

This article was linked to from Hessenberg matrix article, but there is no mention of how it is related, except for the sentence "first motivated by questions in numerical analysis in relation to algorithms for computing eigenvalues and eigenspaces of the linear operator X."

May be it can be touched upon further? - Syockit (talk) 17:54, 20 November 2013 (UTC)[reply]

Well, its obviously "upper triangular", isn't it? What more is there to say? 67.198.37.16 (talk) 10:48, 29 January 2018 (UTC)[reply]

Does the h given define a function?

If the function is supposed to be a map from tuples to tuples then are the domain and range correct? Does that single map define the function for h? That is, can it be literally any map from a n-tuple to another n-tuple? — Preceding unsigned comment added by 2607:EA00:107:2401:A16C:C48F:501B:41CA (talk) 16:40, 11 April 2017 (UTC)[reply]