Matrix Groups

The implementation of Matrix Groups is SageMath is simple. There are a number of these groups that are available to us in SageMath:

• The General Linear Group, denoted in SageMath by $GL(n,F)$
• The Special Linear Group, denoted $SL(n,F)$
• The Orthogonal Group, $GO(n,F)$
• The Special Orthogonal Group, $SO(n,F)$
• The Unitary Group, $GU(n,F)$
• The Special Unitary Group, $SU(n,F)$

Where in each of these $n$ is an integer, and $F$ is a field. In this document we will be using the field $\mathbb{R}$.

The example shown above demonstrates the fact that multiplying by a matrix from the special linear group, area is left unchanged.