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Research Interests:


My main research interests are in the areas of linear algebra, matrix theory, and combinatorics. These interests reside in many areas of mathematics ranging from applied to pure mathematics, and also numerical analysis. I am extremely interested in research problems that have applications or require expertise in overlapping areas of mathematics. I continue to work on problems from combinatorial matrix theory, which, of course, overlap graph theory and linear algebra. Recently, I have been working on a number of different problems, which fall under the headings:

You can find a reasonably current list of my publications via the AMS website at the following link.


For a wonderful description on the history of matrices and determinants written by J. J. O'Conner and E.F. Robertson click here.

Positivity classes of matrices.


  1. totally nonnegative matrices:
  2. determinantal inequalities
  3. eigenvalue location problems
  4. matrix completion problems
  5. matrix inequalities
An m-by-n matrix A is called totally nonnegative (resp. totally positive ) if the determinant of every square submatrix (i.e., minor) of A is nonnegative (resp. positive). The class of totally nonnegative matrices have been well studied and arise in a variety of applications including differential equations, statistics, mathematical biology, approximation theory, integral equations and combinatorics and many others.

In the Spring of 2011 my book (with Charles Johnson) entitled "Totally Nonnegative Matrices" was published by Princeton University Press.

Now that it has been on the market for a little over 9 months, I have received valuable feedback from many people, which I truly appreciate! Inevitably, some of the comments that I have received are of the form of corrections or minor typo's and errors in the book...(many thanks to all of you who have sent along your corrections). I will keep a running list that is linked below as I learn of additional corrections and minor errors.

The working list of Errata for "Totally Nonnegative Matrices" can be found by clicking here.



Combinatorial matrix theory.


  1. algebraic connectivity and related topics:
  2. spectra of graphs
  3. qualitative matrix theory
  4. minimum ranks of graphs
  5. algebraic graph theory
Laplacian matrices of weighted graphs have drawn much attention in recent years, since they arise not only in algebraic graph theory but also in sparse matrix computations and resistive electrical networks.

Student and Postdoctoral Fellow Supervision


Postdoctoral Fellows & Visiting Scholars:



Graduate Students:



Undergraduate Students: