Fig. 4: Generalized inversion (pseudo-inversion) of singular and rectangular matrices using the Miller and DCM architectures.

(Column I) The entries (blue dots) and the eigenvalues (red dots) of a singular \({{{\bf{A}}}}\in {{\mathbb{C}}}^{5\times 5}\) matrix (a polar plot) and the entries of the preconditioned complex symmetric matrix A^*A (b polar plot). The central polar plot c depicts the entries of the pseudoinverse A⁺ (blue dots) compared against the results obtained via the Miller (red dots) and the DCM network architecture, both utilizing the optimum scaling factor \({\alpha }_{\lambda }=\frac{2}{{\lambda }_{1}+{\lambda }_{5}}\approx 0.316\). (Column II) The entries of a binary \({{{\bf{A}}}}\in {{\mathbb{Z}}}^{3\times 5}\) matrix a and the corresponding pseudoinverse b. The bottom figures depict the estimated pseudoinverses via the Miller (c) and the DCM network architecture (d), for α_λ = 0.125 and a feedback coupler with a 30 dB coupling ratio