Solution
= Solution
The statement is true without an additional <rank of a matrix>[rank] assumption. If $A=U\Sigma V^H$ is a <singular value decomposition>, then
$$
(A^\dagger)^H=(V\Sigma^\dagger U^H)^H
=U\Sigma^\dagger V^H=(A^H)^\dagger.
$$
= Solution
The statement is true without an additional <rank of a matrix>[rank] assumption. If $A=U\Sigma V^H$ is a <singular value decomposition>, then
$$
(A^\dagger)^H=(V\Sigma^\dagger U^H)^H
=U\Sigma^\dagger V^H=(A^H)^\dagger.
$$