Kunze Linear Algebra · Problem 10.4.7

Bilinear Forms

Mathematics — Methods · bilinear-form-orthogonal-basis

Problem

Let

V

be the space of all

n \times 1

matrices over

C

and

f

the bilinear form on

V

given by

f(X, Y) = X^t Y

. Let

M

belong to

O(n, C)

. What is the matrix of

f

in the basis of

V

consisting of the columns

M_1, M_2, \ldots, M_n

M