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 \( F \).
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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.