David Allen (3283)

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The Totally Positive Matrix Completion Problem

Hometown: Nashville, Tennessee 

Department: Mathematics 

Advisor: Charles Johnson


A matrix is an array of numbers with a certain number of rows and columns. In each matrix, we can find submatrices, or smaller matrices within it, as well as calculate what is called the determinant of the matrix. My goal is to look at matrices with some unknown entries and determine which of these can be completed in a way so that the determinant of each submatrix is a positive number. This is of interest for many fields including theoretical economics, statistics, and mathematical biology


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