# Answer on Linear Algebra Question for Anurodh

Question #42863

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

A = 1 i 0 B= 1/√2 0 -1/√2

-i 1 1-i 0 1 0

0 1+i 2 V2i 0 V2i

Expert's answer

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.

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