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Kunze Linear Algebra
· Problem 5.4.5
Determinants
Mathematics — Methods · unitary-matrices-determinant
Problem
An
n
×
n
n \times n
n
×
n
matrix
A
A
A
over the field of complex numbers is said to be
unitary
if
A
A
∗
=
I
AA^* = I
A
A
∗
=
I
(
A
∗
A^*
A
∗
denotes the conjugate transpose of
A
A
A
). If
A
A
A
is unitary, show that
∣
det
A
∣
=
1
|\det A| = 1
∣
det
A
∣
=
1
.
Related theory
Hermitian Skew Hermitian And Unitary Matrices
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