You are here

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.


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.

To open this file please click here.

These pdf files are furnished by JSTOR.

Classroom Capsules would not be possible without the contribution of JSTOR.

JSTOR provides online access to pdf copies of 512 journals, including all three print journals of the Mathematical Association of America: The American Mathematical Monthly, College Mathematics Journal, and Mathematics Magazine. We are grateful for JSTOR's cooperation in providing the pdf pages that we are using for Classroom Capsules.

Capsule Course Topic(s):
Linear Algebra | Eigenvalues and Eigenvectors
Average: 2.7 (23 votes)