# Characteristic Polynomials of Magic Squares

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.

Old Node ID:
3528
MSC Codes:
15A04
Author(s):
Ali R. Amir-Moez (Texas Tech University)
Publication Date:
Wednesday, July 14, 2010
Original Publication Source:
Mathematics Magazine
Original Publication Date:
September, 1984
Subject(s):
Algebra and Number Theory
Linear Algebra
Matrix Algebra
Topic(s):
Linear Algebra
Eigenvalues and Eigenvectors
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Rating Count:
17.00
Rating Sum:
46.00
Rating Average:
2.71
Applicable Course(s):
3.8 Linear/Matrix Algebra
Modify Date:
Sunday, November 13, 2011