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Results tagged with matrices
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user 28104
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
15
votes
1
answer
1k
views
Free subgroups of $\mathrm{GL}(2,\mathbb{Z})$
Is there a bound $B$ such that every 2-generator subgroup
$G = \langle a, b \rangle \le {\rm GL}(2,\mathbb{Z})$
whose generators do not satisfy a relation of length $\leq B$ is free?
If it exists, su …
- 19.6k
6
votes
Accepted
Can a block matrix with at least 3 zero blocks of different size on the diagonal and 1's eve...
This can be found with GAP as follows:
First we write a function to build your matrices for given sizes of
diagonal blocks:
ZeroBlockDiagMat := function ( sizes )
local M, k, n, i, j;
M := NullMat …
- 19.6k
6
votes
Deciding if $\mathbb{Z}\ltimes_A \mathbb{Z}^5$ and $\mathbb{Z}\ltimes_B \mathbb{Z}^5$ are is...
Here is Derek Holt's computation done in GAP:
gap> LoadPackage("anupq");
gap> F := FreeGroup("a","b","c","d","e","t");;
gap> AssignGeneratorVariables(F);
gap> comms := List(Combinations(GeneratorsOfGr …
- 19.6k
4
votes
Integer matrix that does not belong to a free group of rank 2
With GAP, you can improve Igor Rivin's answer to rule out all $n$
which are not divisible by $252$:
gap> A := [[2,3],[3,5]];; B := [[5,3],[3,2]];;
gap> G := Group(A*One(Integers mod 252),B*One(Intege …
- 19.6k
3
votes
Computer Algebra Systems that support variable sized matrices
I am not sure what precisely you are looking for, but the GAP
package MatricesForHomalg provides elaborate functionality for
dealing with matrices in the context of homological algebra. …
- 19.6k