Zeros of 2 by 2 Matrix Polynomials

Details Zeros of 2 by 2 Matrix Polynomials Zeros of 2 by 2 Matrix Polynomials

2009-12-05

arxiv.org/abs/0912.1030v1

Mathematics

Rings and Algebras

14 Pages. Research done at an REU at Rutgers Universtiy in 2006 under Robert Wilson

Scientific paper

Consider the $n$th degree polynomial equation, $X^n+A_{n-1}X^{n-1}+...+A_1X+A_0=0$ over the ring of 2 by 2 complex matrices. If this equation has more than ${2n \choose 2}$ solutions, then it has infinitely many solutions. We show here that for any $n,m \in\N$ such that $m\leq{2n \choose 2}$, there exists an $n$th degree polynomial equation with exactly $m$ solutions.

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