Answer to Question #42863 in Linear Algebra for Anurodh

Question

Which of the following matrices are Hermitian and which are Unitary? Justify your answer.


A = 1 i 0 B= 1/√2 0 -1/√2
-i 1 1-i 0 1 0
0 1+i 2 V2i 0 V2i

Answer 1

Matrix A is Hermitian, because ientries are equal to own conjugate transpose. Matrix B is not Hermitian, because conjugate transpose of √2i is equal to -√2i, not -1/√2. Both matrices are not Unitary, because absolute value of every determinant is not equal to one. Determinant of A is equal to -2 , determinant of B is equal to 2i.