Kunze Linear Algebra · Problem 10.2.12

Bilinear Forms

Mathematics — Methods · adjoint-operator-matrix-form

Problem

Let

F

be a field and

V

the space of

n \times 1

matrices over

F

. Suppose

A

is a fixed

n \times n

matrix over

F

and

f

is the bilinear form on

V

defined by

f(X, Y) = X^t A Y

. Suppose

f

is symmetric and non-degenerate. Let

B

be an

n \times n

matrix over

F

and

T

the linear operator on

V

sending

X

into

BX

. Find the operator

T'

of Exercise 11.

Related theory

Adjoint Functors And Freyd S Adjoint Functor Theorem

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