# 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.

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Capsule Course Topic(s):
Linear Algebra | Eigenvalues and Eigenvectors