Abstract
Let G be a group. A group D of square matrices of order n which is homomorphic to G is said to provide an n-dimensional linear representation or a matrix representation of G. One usually calls it simply a representation of G. Thus, if g1 → Ag1, g2 → Ag2 under the mapping where g1, g2 ∈ G and Ag1 Ag2 ∈ D, we demand that $${g_1}{g_2} \to {A_{g1}}{A_{g2}}$$ ((4.1.1)) .
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