ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

## 20th ILAS Conference

Generalized Inverse and its Applications
Organizers: Dragana Cvetkovic Ilic (Faculty of Science and Mathematics, University of Nis); Yimin Wei (Fudan University).

The concept of generalized inverse seems to have been first mentioned in print in 1903 by Fredholm where a particular generalized inverse (called by him pseudoinverse) of an integral operator was given. One year later, in 1904 Hilbert discussed generalized inverses of differential operators. The class of all pseudoinverses was characterized in 1912 by Hurwitz who used the finite dimensionality of the null-space of Fredholm operators to give a simple algebraic construction. Generalized inverses of differential and integral operators thus antedated the generalized inverses of matrices whose existence was first noted by E.H. Moore, who defined a unique inverse, called by him the “general reciprocal”, for every finite matrix. Little notice was taken of Moore’s discovery for 30 years after its first publication, during which time generalized inverses were given for matrices by Siegel and for operators by Tseng, Murray and von Neumann, Atkinson and others. Revival of interest in the subject in the 1950’s centered around the least squares properties of certain generalized inverses which were recognized by Bjerhammar. He rediscovered Moore’s inverse and also noted the relationship of generalized inverses to solutions of linear systems. In 1955 Penrose extended Bjerhammar’s results and showed that Moore’s inverse for a given matrix A is the unique matrix X satisfying the four equations. In Honour of Moore and Penrose this unique inverse is now commonly called Moore-Penrose inverse. Since 1955 thousands of papers on various aspects of generalized inverses and their applications have appeared. Generalized inverses cover a wide range of mathematical areas: matrix theory, operator theory, C*-algebras or rings. Numerous applications include areas such as: statistics, differential equations, numerical analysis, Markov chains, cryptography, control theory, coding theory, incomplete data recovery and robotics.

### Thursday 14/07, 16:00–18:00

1. Thu 16:00–16:30, Room AV 91.20Generalized inverse of tensors via Einstein product, Yimin Wei (Fudan University).
2. Thu 16:30–17:00, Room AV 91.20Solving some open problems on generalized inverses using results on completions of operator matrices, Dragana Cvetkovic Ilic (Faculty of Science and Mathematics, University of Nis).
3. Thu 17:00–17:30, Room AV 91.20Inverses and eigenvalues of diamond alternating sign matrices, Minerva Catral (Xavier University).
4. Thu 17:30–18:00, Room AV 91.20The Bott-Duffin $(e, f)$-inverses and their applications, Yuanyuan Ke (Southeast University).

### Friday 15/07, 10:30–12:30

1. Fri 10:30–11:00, SW RaadzaalRecurrent Neural Network for Computing the W-Weighted Drazin Inverse, Haifeng Ma (Harbin Normal University).
2. Fri 11:00–11:30, SW RaadzaalVarious results concerning the reverse order law for generalized inverses of operators, Jovana Nikolov Radenković (Faculty of Science and Mathematics, University of Nis).
3. Fri 11:30–12:00, SW RaadzaalOn $\{R, s + 1, k, *\}$-potent matrices, Leila Lebtahi (Universitat Politècnica de València).
4. Fri 12:00–12:30, SW RaadzaalCharacterizations and representations of Moore-Penrose inverses, group inverses and core inverses, Jianlong Chen (Southeast University).