ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 22 Apr 2024 04:38:20 +0200Finding minimum sub-algebra that contains a sethttps://ask.sagemath.org/question/77029/finding-minimum-sub-algebra-that-contains-a-set/Hello, I'm trying to understand step 3 in the algorithm 1 provided in the paper "Algebraic Reduction of Hidden Markov Models" by Tommaso Grigoletto and Francesco Ticozzi.
It requires me to compute alg($\mathcal{X}$) and it is defined in the paper like so:
> Let alg($\mathcal{X}$) denote the minimal sub-algebra of $\mathbb{R}^n$ containing the set $\mathcal{X}$.
In example 1 in the paper, the authors give a set $\mathcal{R}$ and the resulting alg($\mathcal{R}$) like this:
$$
\begin{aligned}
& \mathcal{R} = \text{span}\\{\begin{bmatrix} 1/5 & 1/5 & 3/5 \end{bmatrix}\\}\\\\
& \text{alg}(\mathcal{R}) = \text{span}\\{\begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}, \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}\\}
\end{aligned}
$$
> They are all column vectors but I can't seem to give them correct format. It's my first time using this site and Sagemath. Please refer to example 1 at page 8 in the paper.
I need help explaining the definition of alg($\mathcal{X}$). What is "the minimal sub-algebra of $\mathbb{R}^n$ containing the set $\mathcal{X}$"? And how do I turn this into sagemath code? I need a function that input a span like $\mathcal{R}$ and output alg($\mathcal{R}$).Mon, 22 Apr 2024 04:38:20 +0200https://ask.sagemath.org/question/77029/finding-minimum-sub-algebra-that-contains-a-set/