Kunze Linear Algebra · Problem 10.4.4

Bilinear Forms

Mathematics — Methods · orthogonal-group-column-condition

Problem

Let

M

be an

n \times n

matrix over

C

with columns

M_1, M_2, \ldots, M_n

. Show that

M

belongs to

O(n, C)

if and only if

M_j^t M_k = \delta_{jk}.