classical group
groups representable as matrix groups over a real division associative algebra (reals, complexes, or quaternions) that preserve a certain bilinear form (symmetric, skew-symmetric, Hermitian, skew-Hermitian, etc.)
projective unitary group
quotient of special unitary group by its center
unitary group
group of unitary matrices
projective linear group
construction in group theory
special linear group
group of linear transformations with determinant 1
general linear group
n x n invertible matrices over a ring
projective orthogonal group
twofold quotient of the orthogonal group: PO(n) = O(n)/{±1}