[Dd2015] Research opportunity

[Keith Freeland]

Phelim Boyle is looking for a double degree student with strong quantitative skills to work on a research project. Phelim was recently named a fellow of the Royal Society of Canada.
https://uwaterloo.ca/statistics-and-actuarial-science/news/phelim-boyle-named-fellow-royal-society-canada

Below are some details about the research project. If you are interested please email Phelim Boyle pboyle at wlu.ca<mailto:pboyle at wlu.ca>

Analysis of Correlation matrices

This project will investigate  conditions under which correlation matrices have a strictly positive dominant eigenvector. The sufficient conditions, from the Perron-Frobenius theorem, are that all the matrix entries are positive. The conditions for a correlation matrix with some negative entries to have a strictly positive dominant eigenvector are examined . The special structure of correlation matrices permits us to obtain analytical results for low  dimensional matrices.  We will use numerical  methods to examine  the  usefulness of the various  conditions for random correlation  matrices. We also examine the role of the positive definite property in this context.   To succeed  in the this project a student should have a very  strong background in linear algebra and excellent  computing skills.   This project builds on the paper by Boyle and Ndiaye (2018) .

References


Boyle Phelim P and  Thierno  N'Diaye, Correlation Matrices with the Perron Frobenius   Property,   Electronic Journal of Linear Algebra, ISSN 1081-3810 , Volume 34, pp. 240-268, May 2018.



Keith Freeland, PhD, ASA
Director of Business Administration and Mathematics Double Degree Program
Math Business and Accounting Programs, Faculty of Mathematics
University of Waterloo
519-888-4567, ext. 33356
math.uwaterloo.ca/mbus

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