# Characteristic Polynomials of Magic Squares

by Ali R. Amir-Moez (Texas Tech University)

Mathematics Magazine
September, 1984

Subject classification(s): Algebra and Number Theory | Linear Algebra | Matrix Algebra
Applicable Course(s): 3.8 Linear/Matrix Algebra

An $n \times n$ matrix whose rows, columns, and diagonal all sum to the same number $m$ is called magic, and the number $m$ is called the magic sum.  If $A$ is a magic square matrix, then its magic sum $m$ must be an eigenvalue, and hence a characteristic root, of $A$.  A main result of this paper shows that the sum of all the characteristic roots of $A$ except for $m$ must be zero.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.