4
votes
1answer
276 views
+50

Intuition behind the definition of the Siegel-Eichler transformation

Recently I am reading Wall's paper "On the Orthogonal Groups of Unimodular Quadratic Forms II". In this paper, I encountered with the map $E^1_\omega$, which now I am interested in. Let $X$ be an ...
7
votes
0answers
213 views
+50

Hierarchical (Recursive) Random Walk (also known as Hierarchical Hidden Markov Model)

Let us consider the following hierarchical (recursive) random walk model, which is also known as the hierarchical hidden Markov model in computer science (https://en.wikipedia.org/wiki/...
6
votes
0answers
75 views
+100

Matrix semigroups in which a weighted average of eigenvalues is multiplicative

A problem in fractal geometry requires me to consider matrix semigroups with the following curious property. For a $d \times d$ real matrix $A$ let $\lambda_1(A) \geq \lambda_2(A) \geq \cdots \geq \...
3
votes
1answer
122 views
+100

A specific spanning property of a family of vectors

Let $v_1, v_2, v_3, \dots$ be a family of vectors in $\mathbb R^n$ that span $\mathbb R^n$. Given this family, define the family of vectors \begin{align*} \begin{pmatrix} v_1 \\ \alpha_1 v_1 \end{...