Polynomial Equations over Matrices


Polynomial Equations over Matrices

Mentor: Professor Robert L. Wilson

My name: Michael Burger

There is also another Rutgers student working on this project – read her webpage

 

In this project we consider certain polynomial equations over Mk() (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

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