The Magic of Permutation Matrices: Categorizing, Counting and Eigenspectra of Magic Squares

Details The Magic of Permutation Matrices: Categorizing, Counting and Eigenspectra of Magic Squares The Magic of Permutation Matrices: Categorizing, Counting and Eigenspectra of Magic Squares

2010-07-19

arxiv.org/abs/1007.3239v1

Mathematics

History and Overview

26 pages

Scientific paper

Permutation matrices play an important role in understand the structure of magic squares. In this work, we use a class of symmetric permutation matrices than can be used to categorize magic squares. Many magic squares with a high degree of symmetry are studied, including classes that are generalizations of those categorized by Dudeney in 1917. We show that two classes of such magic squares are singular and the eigenspectra of such magic squares are highly structured. Lastly, we prove that natural magic squares of singly-even order of these classes do note exist.

Affiliated with

Also associated with

No associations

Rating

The Magic of Permutation Matrices: Categorizing, Counting and Eigenspectra of Magic Squares does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Magic of Permutation Matrices: Categorizing, Counting and Eigenspectra of Magic Squares, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Magic of Permutation Matrices: Categorizing, Counting and Eigenspectra of Magic Squares will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-63171