Invertible matrices. Or if you think a bit more generally, an invertible linear map.
When the field is not given, it defaults to the real numbers.
Non-invertible are excluded "because" otherwise it would not form a group (every element must have an inverse). This is therefore the largest possible group under matrix multiplication, other matrix multiplication groups being subgroups of it.
general linear group over a finite field of order . Remember that due to the classification of finite fields, there is one single field for each prime power .
Exactly as over the real numbers, you just put the finite field elements into a matrix, and then take the invertible ones.

Articles by others on the same topic (1)

See all articles in the same topic