Assoc ProfessorAnthony Cronin

To see a selected list of my published research articles click on the following ResearchGate link: https://www.researchgate.net/profile/Anthony_Cronin4 A:

Pure Mathematics: My Pure Maths research interests are in Linear Algebra and Matrix Theory. In particular I study the following problems:

(1) The Nonnegative Inverse Eigenvalue Problem (NIEP), this is the problem of finding necessary and sufficient conditions on a list of n complex numbers so that these numbers form the spectra (the list of eigenvalues) of a nonnegative matrix of dimension n. Variants of this problem include the Real Nonnegative Inverse Eigenvalue Problem (RNIEP) and the Symmetric Nonnegative Inverse Eigenvalue Problem (SNIEP) where the list of n numbers is constrained to be real (and the realising matrix to be symmetric).

(2) Integral Similarity of Matrices Given two matrices A and B with integer entries can we decide if these are integrally similar, i.e. can we find an invertible matrix P with integer entries such that P^{-1}AP=B?

(3) The Pascal Matrix I consider the problem of finding the multiplicative order of the matrix S_n which is derived from the Pascal Matrix. B: Mathematics Education In the discipline of Mathematics Education I am interested in mathematics support in Higher Education, in particular the use of Learning Analytics. I also enjoy investigating the research-teaching linkages between the teaching and learning of mathematics (including statistics) at third level and in transitioning from second to third level. I have taught on Adult and Access to Education programmes to non-traditional entry students for over 13 years and I enjoy designing and researching tools (including the use of Technology-Enhanced Learning tools and methods) which can support their learning at third level. I am also interested in how educators at third level can build analytic and self-organised learning skills in students.