He belonged to the academic staff of Pure Mathematics in the Faculty of Sciences at the University of Ghent and was an invited professor at the Universities of Coimbra, Lisbon, Braga, and Brigham Young.

He visited many Universities and attended many International Conferences. In the late sixties, he received a letter from Sir R. Penrose, which contained results on “ A generalized inverse for matrices over the complex numbers “ and started generalizing these results for matrices over general rings and, more generally, for morphisms in general categories.

From then on, he published many international papers about generalized invertibility, the system of von Neumann – Penrose equations and the system of Drazin equations, mainly in The Journal of Linear Algebra and its Applications but also in Linear and Multilinear Algebra, Journal of Pure and Applied Algebra, and Communications in Algebra.

He was and is still strongly interested in the search of a “Unifying Approximation Philosophy “, hidden in Eastern- and Western Philosophies and mirrored by his algebraic categorical results about von Neumann – Penrose regularity that can be found in the following…

Research Publications

R. Puystjens : Over de linkse en rechtse eenheidselementen in een associatieve of niet-
associatieve ring, Simon Stevin Wis-en Natuurkundig Tijdschrift 42 (1969) 171-176

J.A. Thas and R. Puystjens : Number of Regular homographies of a Galois space S(n,q),
Rendiconti di Matematica (2) vol: 3 Serie VI (1970) 1-5

R. Puystjens and J.A. Thas : The Number of Desargues-Configurations of the Projective Plane S(2,q) over the Galois Field GF(q) with characteristic two or three, Simon Stevin Wis-en Natuurkundig Tijdschrift 44 (1971) 160-170

R. Puystjens : Multiplicative Morphisms of Matrix Rings, Analele Stiintifice ale Universitatii
“Al.I.Cuza” din Iasi (1971) 25-28

R. Puystjens : Determinants for matrices over noncommutative rings, Colloquia Mathematica
Societatis Janos Bolyai , 6. Rings, Modules and Radicals,

Keszthely- Hungary (1971) 385-390

R. Puystjens and H. De Smet : The Moore-Penrose Inverse for matrices over Skew Polynomial Rings, Lecture Notes in Mathematics 825 (1980) 94-103

R. Puystjens and D.W. Robinson : The Moore-Penrose inverse of a Morphism with
Factorization, Linear Algebra and its Applications 40 (1981) 129-141

R. Puystjens and J. Van Geel : Diagonalization of Matrices over Graded Principal Domains,
Linear Algebra and its Applications 48 (1982) 265-281

R. Puystjens : Moore-Penrose Inverses for Matrices over some Noetherian Rings, Journal of
Pure and Applied Algebra 31 (1984) 191-198

R. Puystjens and D.W. Robinson : The Moore-Penrose Inverse of a Morphism in an Additive
Category, Communications in Algebra 12 (1984) 287-299

D. Huylebrouck, R. Puystjens and J. Van Geel : The Moore-Penrose Inverse of a Matrix over a Semi-Simple Artinian Ring, Linear and Multilinear Algebra 16 (1984) 239-246

D.W. Robinson and R. Puystjens : EP Morphisms, Linear Algebra and its Applications 64
(1985) 157-174

R. Puystjens and J. Van Geel : On the Diagonalization of von Neumann Regular Matrices, Acta Universitatis Carolinae – Mathematica et Physica 26 (1985) 51-56

D. Huylebrouck and R. Puystjens : Generalized Inverses of a Sum with a Radical Element,
Linear Algebra and its Applications 84 (1986) 289-300

D.W. Robinson and R. Puystjens : Generalized Inverses of Morphisms with Kernels, Linear
Algebra and its Applications 96 (1987) 65-86

D.W. Robinson , R. Puystjens and J. Van Geel : Categories of Matrices with only Obvious
Moore-Penrose Inverses, Linear Algebra and its Applications 97 (1987) 93-102

R. Puystjens : Some aspects of Generalized Invertibility, Bulletin de la Société Mathématique de Belgique XL (1988) 67-72

R. Puystjens : On a Generalization of the Kernel Theorem for Moore-Penrose Invertibility of
Morphisms, Linear Algebra and its Applications 117 (1989) 168-171

R. Puystjens and D.W. Robinson : Symmetric Morphisms and the Existence of Moore-
Penrose Inverses, Linear Algebra and its Applications 131 (1990) 51-69

R. Puystjens and M.C. Gouveia : About the Group Inverse and Moore-Penrose inverse of a
Product, Linear Algebra and its Applications 150 (1991) 361-369

R. Puystjens and R.E. Hartwig : The Group Inverse of a Companion Matrix, Linear and
Multilinear Algebra 43 (1997) 137-150

P. Patrício and R. Puystjens : About the von Neumann regularity of triangular block matrices,
Linear Algebra and its Applications 332-334 (2001) 485-502

R.E. Hartwig, P. Patrício and R. Puystjens : Diagonalizable triangular matrices in rings of
triangular matrices, Linear Algebra and its Applications (2004) 371-379

P.Patrício and R. Puystjens :Generalized invertibility in two semigroups of a ring, Linear
Algebra and its applications 377 (2004) 125-139

R. Puystjens and M.C. Gouveia: Drazin invertibility for matrices over an arbitrary ring, Linear
Algebra and its Applications 385 (2004) 105-116

P. Patrício and R. Puystjens: Drazin-Moore-Penrose invertibility in rings, Linear Algebra and
its Applications (2004)

R.E. Hartwig, P. Patricio and R. Puystjens : Diagonalizing triangular matrices via orthogonal
Pierce decompositions, Linear algebra and its Applications 401 (2005) 381-391