stylistic:style_transfer
Generalizations

The complex -valued matrices analogous to real orthogonal matrices are the unitary matrices U (n) {\displaystyle \mathrm {U} (n)}, which represent rotations in complex space. The set of all unitary matrices in a given dimension n forms a unitary group U (n) {\displaystyle \mathrm {U} (n)} of degree n; and its subgroup representing proper rotations (those that preserve the orientation of space) is the special unitary group S U (n) {\displaystyle \mathrm {SU} (n)} of degree n. These complex rotations are important in the context of spinors. The elements of S U (2) {\displaystyle \mathrm {SU} (2)} are used to parametrize three -dimensional Euclidean rotations (see above), as well as respective transformations of the spin (see representation theory of SU(2)).