Let K {\displaystyle {}K} be a field, and let M = ( a i j ) i j {\displaystyle {}M=(a_{ij})_{ij}} be an m × n {\displaystyle {}m\times n} -matrix over K {\displaystyle {}K} . Then the n × m {\displaystyle {}n\times m} -matrix
is called the transposed matrix of M {\displaystyle {}M} .