Let K {\displaystyle {}K} be a field, and n ∈ N + {\displaystyle {}n\in \mathbb {N} _{+}} . An orthogonal n × n {\displaystyle {}n\times n} -matrix M {\displaystyle {}M} fulfilling
is called a special orthogonal matrix. The set of all special orthogonal matrices is called special orthogonal group; it is denoted by SO n ( K ) {\displaystyle {}\operatorname {SO} _{n}\!{\left(K\right)}} .
