Let V be the space of all matrices over C and f the bilinear form on V given by . Let Ab belong to O(n, C). What is the matrix off in the basis of I’ consisting of the columns of M?
Let is the space of all matrices over and the bilinear form on given by and let belong to , that is
Let are columns of matrix , such that
each is column vector,
each is row vector, then consider ,