Polynomial Equations over Matrices
My name: Michael Burger
There is also another
In this project we consider certain polynomial equations over Mk(ℂ) (matrices with complex entires and size k x k), namely those of the form:
Xn + An-1Xn-1 + ...... + A0 = 0, where 0 is understood to be the (k x k) zero matrix and (Ai are k x k coefficient matrices, and X is the k x k matrix that solves the equation.)
Some
research has already been done on this issue. Most relevant to the current aim
of this project is the research about finding solutions to the above equation
in the case where k = n = 2. The following paper: Polynomial
Equations over Matrices by my
mentor Professor Wilson of the Rutgers
Mathematics Department is the primary reference for this project.
Updates: (well, some of them…)
I
created
several examples to prove the existence
of polynomial equations with
certain numbers of solutions, and also as a spring board for some of the
conjectures that have been proved during the course of this
program! I have proved a few useful results: if you would like to
learn more about them, please feel free to email me and I will send
you the pdf!
email:
myfirstname.mylastname AT gmail.com