Memristive Linear Algebra

The paper’s treatment of the Drazin case is mathematically incorrect: it asserts convergence of α∫_0^∞ e^{−αtA}dt for positive semidefinite A and identifies ∫_0^∞ e^{−As}ds with the Drazin inverse AD, both of which fail when A is singular (the integral diverges along Null(A)). The model correctly diagnoses this, provides the missing spectral assumptions for convergence of the linear matrix ODE, and gives a sound flow for the Moore–Penrose pseudoinverse. The pseudoinverse part and the general stable M case in the paper are otherwise aligned with the model, but the paper’s Drazin claims require major correction. Key statements in the paper that are erroneous include: “the improper integral converges because A is positive semi-definite” and “R(∞)=∫_0^∞ e^{−As}ds=AD is the definition of the Drazin inverse”. By contrast, the model’s analysis correctly shows divergence along the nullspace unless the forcing is projected onto Range(A), and it supplies the standard stability condition Re σ(M)>0 for the general flow. See the paper’s eqs. (7)–(9) and bullets on M,E choices, the Appendix A ‘Drazin inverse’ subsection, and Appendix B eq. (B11) for the problematic claims, and the Appendix A ‘Moore–Penrose’ subsection for the correct Showalter formula used in (b) (citations: ).