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1:11 PM
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Q: How to prove that $\exists u_1\in P_n$ s.t $y[u_1]$ is minimal and there are finitely many $u_1=(g_1,...,g_n) \in \Bbb Z^n$ s.t $gcd(g_1,...,g_n)=1$

user152715If $P_n=\{y\in M(n,\Bbb R)|$ $y$ is positive definite and symmetric $\}$ then for a fixed $y \in P_n$ consider the set $A=\{y[u]|u \in \Bbb Z^n\}$ where $y[u]=u^tyu$ is clearly positive. Now, how to prove that $\exists u_1\in P_n$ s.t $y[u_1]$ is minimal element of the set $A$ and there are finit...

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Q: Problem on Minkowski's reduction theory of positive definite matrix

user152715I am facing problem to understand Minkowski's reduction theory from Klingen's Siegel Modular form book. I am giving the pictures of the corresponding pages. I am stuck there for hours. $P_n=\{y\in M(n,\Bbb R)| y>0\}$ Now my question is "What does minimal mean where he states "$y[u_1]$ be...

@JohnMa Well, I am not sure. The possibilities are either removing it unilaterally or opening a discussion on meta about the new tag first.
We will see whether some other users who visit this room have an opinion on . (And on the distinction you mentioned in your message.)
19 hours ago, by John Ma
More importantly, the study of spectral theory for matrices are trivial: one just use Jordan canonical form. Grouping these trivial questions with the non-trivial one in spectral theory/operator theory seems un-necessary.
 

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