My research interests are mainly in Matrix Analysis and Operator Theory. I worked on several problems in the 2 topics. One of the research problems I have worked on for many years is the “theory of complex matrices with variants of the diagonal dominance property.” The problem can be shown to be closely linked to the 2 problems of “establishing inclusion regions for the spectrum of a matrix” and “investigating the spectrum of some perturbed linear operators.” I published 9 papers related to the 3 problems. Some of the papers are long and substantial, like my 2 published papers in the journal “Linear Algebra and its Applications” in the years 1995 and 2019. My work involves dealing with finite square matrices, and infinite matrices (acting as linear operators on linear subspaces of complete sequence spaces). The elegant theory has several useful applications, including the solutions of linear systems and solving Mathieu’s differential equation.
I have also worked on the problem of solving systems of matrix equations, with the matrices having either complex or quaternion entries. I have several joint papers on the topic.
My joint paper with Qing-Wen Wang and Fuzhen Zhang: “F.O. Farid, Qing-Wen Wang and Fuzhen Zhang, On the eigenvalues of quaternion matrices, Linear and Multilinear Algebra, Volume 59, Issue 4, (2011) 451-473” is a highly influential paper in the topic of its investigation.
My paper: “F.O. Farid, On the deformation of linear r-fields, Linear Algebra and Its Applications, Volume 429, Issue 1, (2008) 249-265” solved a problem that remained unsolved for more than 85 years.
I also worked on “numerical range problems” for linear operators and operator polynomials, and published 2 papers related to the 2 problems in 1999 and 2002.
My joint paper with the famous late mathematician K. Varadarajan: “F.O. Farid and K. Varadarajan, Isometric Shift Operators on C(X), Canadian Journal of Mathematics, Volume 46, Issue 3, (1994) 532-542” is a highly influential paper in Operator Theory and Functional Analysis.
I worked on the “spectral variation problem.” This is a hard problem that few mathematicians were able to contribute to. I published a paper on the problem in the journal “Linear Algebra and its Applications” in the year 1992.
Recently, I became interested in Bibliometrics, and I derived a new research assessment measure that addresses several flaws of the popular h-index and some other research performance indicators such as publication counts, citation counts and the g-index.
Contact Farid at farid “dot” farid at-sign ronininstitute [dot] org