Linear group
General linear group and representation theory [ edit ] Main articles: General linear group , Representation theory , and Character theory Two vectors (the left illustration) multiplied by matrices (the middle and right illustrations). The middle illustration represents a clockwise rotation by 90°, while the right-most one stretches the � -coordinate by factor 2. Matrix groups consist of matrices together with matrix multiplication . The general linear group G L ( � , � ) consists of all invertible � -by- � matrices with real entries. [61] Its subgroups are referred to as matrix groups or linear groups . The dihedral group example mentioned above can be viewed as a (very small) matrix group. Another important matrix group is the special orthogonal group S O ( � ) . It describes all possible rotations in � dimensions. Rotation mat...