@article(azumaya1954strongly, author = {G. Azumaya}, year = {1954}, title = {Strongly $\pi$-regular rings}, journal = {Journal of the Faculty of Science Hokkaido University. Ser. 1 Mathematics}, volume = {13}, number = {1}, pages = {034--039}, url = {http://hdl.handle.net/2115/55983}, ) @article(baksalary2021moore, author = {O. M. Baksalary and G. Trenkler}, year = {2021}, title = {The Moore--Penrose inverse: a hundred years on a frontline of physics research}, journal = {The European Physical Journal H}, volume = {46}, pages = {1--10}, doi = {10.1140/epjh/s13129-021-00011-y}, ) @inproceedings(EPTCS143.2, author = {M. Bartha}, year = {2014}, title = {Quantum Turing automata}, editor = {Benedikt L\"owe and Glynn Winskel}, booktitle = {{\rm Proceedings 8th International Workshop on} Developments in Computational Models, {\rm Cambridge, United Kingdom, 17 June 2012}}, series = {Electronic Proceedings in Theoretical Computer Science}, volume = {143}, publisher = {Open Publishing Association}, pages = {17--31}, doi = {10.4204/EPTCS.143.2}, ) @book(campbell2009generalized, author = {S. Campbell and C. Meyer}, year = {2009}, title = {Generalized inverses of linear transformations}, publisher = {SIAM}, doi = {10.1137/1.9780898719048}, ) @article(cao2021nisq, author = {N. Cao and J. Lin and D. Kribs and Y.-T. Poon and B. Zeng and R. Laflamme}, year = {2021}, title = {NISQ: Error correction, mitigation, and noise simulation}, journal = {arXiv preprint arXiv:2111.02345}, ) @article(chen2023optimal, author = {J. Chen and Y. Wang and J. Chen and S. Su}, year = {2023}, title = {Optimal figure of merit of low-dissipation quantum refrigerators}, journal = {Physical Review E}, volume = {107}, number = {4}, pages = {044118}, doi = {10.1103/PhysRevE.107.044118}, ) @article(chen2021extrapolating, author = {J.-F. Chen and C. Sun and H. Dong}, year = {2021}, title = {Extrapolating the thermodynamic length with finite-time measurements}, journal = {Physical Review E}, volume = {104}, number = {3}, pages = {034117}, doi = {10.1103/PhysRevE.104.034117}, ) @inproceedings(EPTCS384.10, author = {J.R.B. Cockett and J-S. P. Lemay}, year = {2023}, title = {{Moore-Penrose Dagger Categories}}, booktitle = {{\rm Proceedings of the Twentieth International Conference on} Quantum Physics and Logic, {\rm Paris, France, 17-21st July 2023}}, series = {Electronic Proceedings in Theoretical Computer Science}, volume = {384}, publisher = {Open Publishing Association}, pages = {171--186}, doi = {10.4204/EPTCS.384.10}, ) @article(cockett2024drazin, author = {R. Cockett and J.-S. P. Lemay and P. V. Srinivasan}, year = {2024}, title = {{Drazin Inverses in Categories}}, journal = {Theory and Applications of Categories}, volume = {43}, number = {14}, pages = {455--519}, url = {http://www.tac.mta.ca/tac/volumes/43/14/43-14abs.html}, ) @article(drazin1958pseudo, author = {M. P. Drazin}, year = {1958}, title = {Pseudo-inverses in associative rings and semigroups}, journal = {The American mathematical monthly}, volume = {65}, number = {7}, pages = {506--514}, doi = {10.2307/2308576}, ) @article(Fitting1933, author = {H. Fitting}, year = {1933}, title = {Die Theorie der Automorphismenringe Abelscher Gruppen und ihr Analogon bei nicht kommutativen Gruppen}, journal = {Mathematische Annalen}, volume = {107}, pages = {514--542}, doi = {10.1007/BF01448909}, ) @book(heunen2009categorical, author = {C. Heunen}, year = {2009}, title = {Categorical quantum models and logics}, publisher = {Amsterdam University Press}, doi = {10.5117/9789085550242}, ) @book(heunen2019categories, author = {C. Heunen and J. Vicary}, year = {2019}, title = {{Categories for Quantum Theory: an Introduction}}, publisher = {Oxford University Press}, doi = {10.1093/oso/9780198739623.001.0001}, ) @article(jacobs2009categorical, author = {B. Jacobs and C. Heunen and I. Hasuo}, year = {2009}, title = {Categorical semantics for arrows}, journal = {Journal of functional programming}, volume = {19}, number = {3-4}, pages = {403--438}, doi = {10.1017/S0956796809007308}, ) @article(King1977ANO, author = {C. F. King}, year = {1977}, title = {{A note on Drazin inverses}}, journal = {Pacific Journal of Mathematics}, volume = {70}, pages = {383--390}, doi = {10.2140/pjm.1977.70.383}, ) @article(leinster2022eventual, author = {T. Leinster}, year = {2023}, title = {The eventual image}, journal = {Theory and Applications of Categories}, url = {http://www.tac.mta.ca/tac/volumes/42/9/42-09abs.html}, ) @article(miller2019work, author = {H. Miller and M. Scandi and J. Anders and Perarnau-Llobet, M.}, year = {2019}, title = {Work fluctuations in slow processes: quantum signatures and optimal control}, journal = {Physical review letters}, volume = {123}, number = {23}, pages = {230603}, doi = {10.1103/PhysRevLett.123.230603}, ) @article(moore1920reciprocal, author = {E. H. Moore}, year = {1920}, title = {On the reciprocal of the general algebraic matrix}, journal = {Bull. Am. Math. Soc.}, volume = {26}, pages = {394--395}, doi = {10.1090/S0002-9904-1920-03322-7}, ) @inproceedings(munn1961pseudo, author = {W. D. Munn}, year = {1961}, title = {Pseudo-inverses in semigroups}, booktitle = {Mathematical Proceedings of the Cambridge Philosophical Society}, volume = {57}, organization = {Cambridge University Press}, pages = {247--250}, doi = {10.1017/S0305004100035143}, ) @inproceedings(penrose1955generalized, author = {R. Penrose}, year = {1955}, title = {A generalized inverse for matrices}, booktitle = {Mathematical proceedings of the Cambridge philosophical society}, volume = {51}, organization = {Cambridge University Press}, pages = {406--413}, doi = {10.1017/S0305004100030401}, ) @article(puystjens2004drazin, author = {R. Puystjens and M.C. Gouveia}, year = {2004}, title = {Drazin invertibility for matrices over an arbitrary ring}, journal = {Linear algebra and its applications}, volume = {385}, pages = {105--116}, doi = {10.1016/S0024-3795(03)00618-9}, ) @article(puystjens1981moore, author = {R. Puystjens and D. w. Robinson}, year = {1981}, title = {The Moore-Penrose inverse of a morphism with factorization}, journal = {Linear Algebra and its Applications}, volume = {40}, pages = {129--141}, doi = {10.1016/0024-3795(81)90145-2}, ) @article(puystjens1984moore, author = {R. Puystjens and D. W. Robinson}, year = {1984}, title = {The Moore-Penrose inverse of a morphism in an additive category}, journal = {Communications in algebra}, volume = {12}, number = {3}, pages = {287--299}, doi = {10.1080/00927878408823004}, ) @article(robinson1985ep, author = {R. Puystjens and D. W. Robinson}, year = {1985}, title = {EP morphisms}, journal = {Linear algebra and its applications}, volume = {64}, pages = {157--174}, doi = {10.1016/0024-3795(85)90273-3}, ) @article(robinson1987generalized, author = {R. Puystjens and D. W. Robinson}, year = {1987}, title = {Generalized inverses of morphisms with kernels}, journal = {Linear Algebra and Its Applications}, volume = {96}, pages = {65--86}, doi = {10.1016/0024-3795(87)90336-3}, ) @article(puystjens1990symmetric, author = {R. Puystjens and D. W. Robinson}, year = {1990}, title = {Symmetric morphisms and the existence of Moore-Penrose inverses}, journal = {Linear Algebra and Its Applications}, volume = {131}, pages = {51--69}, doi = {10.1016/0024-3795(90)90374-L}, ) @article(selinger2007dagger, author = {P. Selinger}, year = {2007}, title = {Dagger compact closed categories and completely positive maps}, journal = {Electronic Notes in Theoretical computer science}, volume = {170}, pages = {139--163}, doi = {10.1016/j.entcs.2006.12.018}, ) @article(wang2017class, author = {Z. Wang}, year = {2017}, title = {A class of Drazin inverses in rings}, journal = {Filomat}, volume = {31}, number = {6}, pages = {1781--1789}, doi = {10.2298/FIL1706781W}, ) @article(wei2003representation, author = {Y. Wei and S. Qiao}, year = {2003}, title = {{The representation and approximation of the Drazin inverse of a linear operator in Hilbert space}}, journal = {Applied Mathematics and Computation}, volume = {138}, number = {1}, pages = {77--89}, doi = {10.1016/S0096-3003(02)00100-5}, ) @article(wu2014remarks, author = {Z. Wu and S. Zhang and C. Zhu}, year = {2014}, title = {Remarks on generalized quantum gates}, journal = {Hacettepe Journal of Mathematics and Statistics}, volume = {43}, number = {3}, pages = {451--460}, url = {https://dergipark.org.tr/tr/download/article-file/649195}, )