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

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 326 / 1 / b / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-326/1/b/i/solution