1
vote
0answers
33 views

Intuitively what is it if making a modification of a torus?

It is well-known that if we have a equivalence relation in $\mathbb{R}^2$:$(z_1,z_2)\sim (z_1',z_2')$ iff $$\begin{pmatrix} z_1'\\ z_2' \\ \end{pmatrix}=\begin{pmatrix} 1&0\\ 0&1 \\ ...
1
vote
1answer
167 views

Siegel upper-half space

In dimension 1, the Siegel upper-half space $\mathbb{H}=\{\tau\in\mathbb{C}:\Im\tau>0\}$ has the property that if $\lambda\in\mathbb{C}^\times$, then $a\lambda\in\mathbb{H}$ for some ...
2
votes
0answers
71 views

Eigenvalue of a form

I came across the following matrix while reading an article..Can you please help me to understand the following. We are defining following form: ...
7
votes
1answer
326 views

Holomorphic function of a matrix

A statement is made below. The questions are: (a) Is the statement true? (b) If it is, does it appear in the literature? Here is the statement. For any matrix $A$ in $M_n(\mathbb C)$, write ...