On most perfect magic squares of order four

A simple parametrization for most perfect magic (MPM) squares is derived. This parametrization permits to calculate their powers and eigenvalues as well as their Moore-Penrose, group, and core inverses in an easy fashion. Such properties as EP-ness, normality, symmetry, and partial isometriness of t...

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Published inLinear & multilinear algebra Vol. 68; no. 7; pp. 1411 - 1423
Main Authors Baksalary, Oskar Maria, Trenkler, Dietrich, Trenkler, Götz
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.07.2020
Taylor & Francis Ltd
Subjects
Eigenvalues
eigenvalues and eigenspaces
generalized inverses
Matrix classes
Normality
Parameterization
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Abstract A simple parametrization for most perfect magic (MPM) squares is derived. This parametrization permits to calculate their powers and eigenvalues as well as their Moore-Penrose, group, and core inverses in an easy fashion. Such properties as EP-ness, normality, symmetry, and partial isometriness of the MPM squares are also characterized. Moreover, their eigenspaces are identified along with some properties of such squares with prime entries.
AbstractList A simple parametrization for most perfect magic (MPM) squares is derived. This parametrization permits to calculate their powers and eigenvalues as well as their Moore–Penrose, group, and core inverses in an easy fashion. Such properties as EP-ness, normality, symmetry, and partial isometriness of the MPM squares are also characterized. Moreover, their eigenspaces are identified along with some properties of such squares with prime entries.
A simple parametrization for most perfect magic (MPM) squares is derived. This parametrization permits to calculate their powers and eigenvalues as well as their Moore-Penrose, group, and core inverses in an easy fashion. Such properties as EP-ness, normality, symmetry, and partial isometriness of the MPM squares are also characterized. Moreover, their eigenspaces are identified along with some properties of such squares with prime entries.
Author Baksalary, Oskar Maria
Trenkler, Dietrich
Trenkler, Götz
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  fullname: Trenkler, Götz
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Snippet A simple parametrization for most perfect magic (MPM) squares is derived. This parametrization permits to calculate their powers and eigenvalues as well as...
A simple parametrization for most perfect magic (MPM) squares is derived. This parametrization permits to calculate their powers and eigenvalues as well as...
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SubjectTerms Eigenvalues
eigenvalues and eigenspaces
generalized inverses
Matrix classes
Normality
Parameterization
Title On most perfect magic squares of order four
URI https://www.tandfonline.com/doi/abs/10.1080/03081087.2018.1545005
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Volume 68
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