Research Experiences for Undergraduates (REU) Seminar

Topic: Polynomial Equations Over Matrices
Speaker: Robert Wilson, Associate Dean and Professor of Mathematics, Rutgers University
Date and time: Friday, June 29, 2001, 12:00 noon
Location: DIMACS Center, Room 431, Rutgers University, Piscataway, NJ

Lunch will be served

A well-known result of elementary algebra states that if a and b are complex numbers, then the quadratic equation

x2 + ax + b = 0

has at most two solutions in complex numbers.

We will consider the same problem where a, b, and x are two-by-two matrices over the complex numbers. We will solve this problem using basic ideas from linear algebra: eigenvectors, eigenvalues and determinants. The solution generalizes to equations of degree m

xm + am-1xm-1 + ... + a1x + a0 = 0

where x and the ai are n-by-n matrices over the complex numbers.

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