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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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Publish Page: 
Furnished by JSTOR: 
File Content: 
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
Average: 2.8 (18 votes)

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