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Characteristic Polynomials of Magic Squares

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

This article originally appeared in:
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
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