The General Linear Group, denoted as \( \text{GL}(n, F) \), is a fundamental concept in linear algebra and group theory. It consists of all invertible \( n \times n \) matrices with entries from a field \( F \).

Ancestors (5)

  1. Abstract algebra
  2. Algebra
  3. Fields of mathematics
  4. Mathematics
  5. Home

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (1)

General linear group by Ciro Santilli 37 Updated 2025-07-16
View more
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.
Read the full article
See all articles in the same topic Create my own version