# Exercise 2.30

Suppose $A$ is a $m\times m$ Hermitian operator and $B$ is a $n\times n$ Hermitian operator, we could obtain tensor product between $A$ and $B$ as $A\otimes B$, and the adjoint conjugate of $A\otimes B$ as

$$
(A\otimes B)^{\dagger} = A^{\dagger}\otimes B^{\dagger} =  A\otimes B
$$(eqn:2.30.1)

where we use $A^{\dagger} = A $ and $B^{\dagger}= B$. Thus, we conclude that the tensor product of two Hermitian operators is Hermitian.