The Moore-Penrose inverse of matrices with an acyclic bipartite graph (Q1886523)

For any \((m \times n)\)-matrix \(A\), the Moore-Penrose inverse \(A^\dagger\) is the unique matrix that satisfies the following four properties: \(A^\dagger A A^\dagger = A^\dagger\), \(A A^\dagger A = A\), \((A^\dagger A)^T = A^\dagger A\), \((AA^\dagger)^T = AA^\dagger\). The authors study the Moore-Penrose inverse of nearly reducible matrices.