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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Bibliographic Details
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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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2018.1545005