2012 Student Research Conference:

25th Annual Student Research Conference

25th Annual Student Research Conference

**A Novel Matrix Decomposition **

Laipeng Zheng

Dr. Michael Adams , Faculty Mentor

We study a novel matrix decomposition motivated by demographic loop analysis. Loop analysis is an analytic technique of interest to ecologists in the study of population dynamics. We have found that a loop decomposition of the elasticity matrix induces a corresponding decomposition of the population projection matrix into a sum of matrices we refer to as cyclic summands. We have determined that the vector space generated by the cyclic summands has the same dimension as the cycle space of the digraph associated with the population projection matrix. We have also carried out computer simulations to investigate the relationship between the eigenvalues of the population projection matrix and those of the cyclic summands.

**Keywords:** loop analysis, matrix , elasticity , population , digraph , biology , cyclic summands, projection

**Topic(s):**Mathematics

**Presentation Type:** Oral Paper

**Session:** 210-1

**Location:** VH 1228

**Time:** 9:30