Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Kunze Linear Algebra
· Problem 10.1.12
Bilinear Forms
Mathematics — Methods · bilinear-form-linear-operators
Problem
Let
f
f
f
,
g
g
g
be bilinear forms on a finite-dimensional vector space
V
V
V
. Suppose
g
g
g
is non-singular. Show that there exist unique linear operators
T
1
T_1
T
1
,
T
2
T_2
T
2
on
V
V
V
such that
f
(
α
,
β
)
=
g
(
T
1
α
,
β
)
=
g
(
α
,
T
2
β
)
f(\alpha, \beta) = g(T_1 \alpha, \beta) = g(\alpha, T_2 \beta)
f
(
α
,
β
)
=
g
(
T
1
α
,
β
)
=
g
(
α
,
T
2
β
)
for all
α
\alpha
α
,
β
\beta
β
.
Related theory
Linear Operators Bounded And Unbounded
Browse the problem library