= General linear group
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= $GL(n)$
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= $GL(n, F)$
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Invertible matrices. Or if you think a bit more generally, an invertible <linear map>.
When the <field (mathematics)> $F$ is not given, it defaults to the <real numbers>.
Non-invertible are excluded "because" otherwise it would not form a <group (mathematics)> (every element must have an inverse). This is therefore the largest possible group under <matrix multiplication>, other matrix multiplication groups being subgroups of it.