Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Kunze Linear Algebra
· Problem 8.3.5
Inner Product Spaces
Mathematics — Methods · adjoints-invertible
Problem
Let
V
V
V
be a finite-dimensional inner product space and
T
T
T
a linear operator on
V
V
V
. If
T
T
T
is invertible, show that
T
∗
T^*
T
∗
is invertible and
(
T
∗
)
−
1
=
(
T
−
1
)
∗
(T^*)^{-1} = (T^{-1})^*
(
T
∗
)
−
1
=
(
T
−
1
)
∗
.
Browse the problem library