In
mathematics, a
matrix group is a
group G consisting of
invertible matrices over some
field K, usually fixed in advance, with operations of
matrix multiplication and inversion. More generally, one can consider
n ×
n matrices over a
commutative ring R. (The size of the matrices is restricted to be finite, as any group can be represented as a group of infinite matrices over any field.) A
linear group is an abstract group that is isomorphic to a matrix group over a field
K, in other words, admitting a
faithful, finite-dimensional
representation over
K.