Event Title
Fixed Point Theory of Matrix Families
Faculty Mentor
Tilak deAlwis
Location
Hamilton Hall 223
Session
Session 2
Start Date
11-4-2014 1:00 PM
End Date
11-4-2014 2:00 PM
Description
In this paper, we investigated the behavior of the characteristic polynomials of a one-parameter family of 2x2 matrices. By doing so, we observed that these characteristic polynomials pass through a fixed point on the xy-plane. We generalized this observation to a one-parameter family of 2x2 matrices to discover a connection between the fixed points and the eigenvalues of certain sub-matrices. Afterwards, we considered the locus of the critical points of the characteristic polynomials of 2x2 and 3x3 families of matrices, including a family containing arbitrary linear functions. We used Mathematica® to discover and illustrate our results through animations.
Fixed Point Theory of Matrix Families
Hamilton Hall 223
In this paper, we investigated the behavior of the characteristic polynomials of a one-parameter family of 2x2 matrices. By doing so, we observed that these characteristic polynomials pass through a fixed point on the xy-plane. We generalized this observation to a one-parameter family of 2x2 matrices to discover a connection between the fixed points and the eigenvalues of certain sub-matrices. Afterwards, we considered the locus of the critical points of the characteristic polynomials of 2x2 and 3x3 families of matrices, including a family containing arbitrary linear functions. We used Mathematica® to discover and illustrate our results through animations.