 Projective linear group

The projective linear group is $PG{L}_n(F)=G{L}_n(F)/F^{\times }$ and acts on projective space.

The projective linear group, denoted as \( \text{PGL}(n, F) \), is a fundamental concept in algebraic geometry and linear algebra. It is defined as the group of linear transformations of a projective space, and its structure relates closely to the field \( F \) over which the vectors are defined. Here's a more detailed explanation: ### Definition 1.

TODO motivation. Motivation. Motivation. Motivation. The definitin with quotient group is easy to understand.