Remarks on generalized magic squares of order 3

Leonard Daus, Andrei Vasilescu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A generalized magic square of order n is an n by n array of numbers whose rows, columns, and the two diagonals sum to k, called the magic sum. In the first part of this paper, we give several elementary properties of generalized magic squares of order 3. In the second part we prove that any generalized magic square of order 3 is a -t EP element if and only if the magic sum S * of the adjoint matrix A * is a non-zero number. As a consequence, the group inverse of generalized magic square is also a generalized-magic square, when the adjoint matrix has the magic sum non-zero.
Original languageEnglish
Title of host publicationTrends and challenges in applied mathematics. Conference proceedings of the international conference, ICTCAM 2007
EditorsGavriil Paltineanu, Emil Popescu
PublisherMatrix Rom, Bucharest
ISBN (Print)978-973-755-283-9
Publication statusPublished - 2007
EventTrends and challenges in applied mathematics - Bucharest, Romania
Duration: Jun 20 2007 → …

Conference

ConferenceTrends and challenges in applied mathematics
Period6/20/07 → …

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