Kunze Linear Algebra · Problem 10.1.9

Bilinear Forms

Mathematics — Methods · radical-of-bilinear-form

Problem

Let

f

be the bilinear form defined in Exercise 6. Let

W

be the set of all matrices

A

V

such that

f(A, B) = 0

for all

B

. Show that

W

is a subspace of

V

. Describe

W

explicitly and find its dimension.