Diagrammatic presentation of inner and outer inverses: \(S\)-diagrams (Q1301307)

The entire range of generalized inner and outer matrix inverses in diagram forms is considered. \(S\)-diagrams are constructed. The notion of a ladder is introduced. Equivalence relations between inner and outer inverses are discussed and represented in diagrams. As examples two matrix inverses are studied: \(A_0=\text{diag}(1,1,0)\), \(G_{0(1)} =\text{diag} (1,1,0)\) and \(X=\text{diag}(1,0,0)\), \(A_0=\text{diag}(1,1,0)\). The 32 inner inverses of \(A_0\) and the 24 outer inverses of \(A_0\) are tabulated.