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Journals / İstatistik Araştırma Dergisi / 2026 / Cilt: 2 Sayı: 2

Some Remarks on the Eigenvalues of the Magic Matrices and Moore-Penrose Inverse

Sihirli Kare Matrislerin Öz Değerlerinin İncelenmesi ve Moore-Penrose İnversi

Fikri Akdeniz(ÇUKUROVA ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ, İSTATİSTİK BÖLÜMÜ)
Asuman Türkmen(ÇUKUROVA ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ, MATEMATİK BÖLÜMÜ)
Pages
7–15
Publication Date
2003-08-17
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also examine the eigenvalues and the Moore- Penrose inverses of singular magic square matrices

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we consider some nxn magic or semi-magic (real) square matrices.
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Key Findings & Data:In this paper we consider some nxn magic or semi-magic (real) square matrices.
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Conclusion & Impact:We also examine the eigenvalues and the Moore- Penrose inverses of singular magic square matrices
🔬Design:Konferans Bildirisi
📍Scope:Comprehensive Sample
⚙️Variables:Moore-Penrose Inversi · Öz Değer · Sihirli Kare

Abstract

In this paper we consider some nxn magic or semi-magic (real) square matrices. We also examine the eigenvalues and the Moore- Penrose inverses of singular magic square matrices

Özet

Bu çalışmada nxn biçimindeki reel girişlere sahip bazı sihirli ya da yarı-sihirli kare matrisleri inceleyeceğiz. Singüler olan matrislerin öz değerlerini ve Moore-Penrose inverslerini vereceğiz.

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Cite This Article

Akdeniz, F., Türkmen, A. (2003). Some Remarks on the Eigenvalues of the Magic Matrices and Moore-Penrose Inverse. İstatistik Araştırma Dergisi, Cilt: 2 Sayı: 2, 7–15. https://ajindex.com/articles/1617966

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References (5)

  1. BOOTH, A. D. and BOOTH, K.H.V. (1955). On magic Squares. The Mathematical Gazette, 39, 132-133.
  2. PASLES, P.C. (2001). The Lost Squares of Dr. Franklin: Ben Franklin's Missing Squares and the Secret of the Magic Circle. The American Mathematical Monthly, 108, 489-511.
  3. RAO, C. R. and MITRA, S. K. (1971). Generalized Inverse of Matrices and Its Applications, New York: John Wiley.
  4. SCHMIDT, K. and TRENKLER, G. (2001) The Moore-Penrose Inverse of a Semi-Magic Square is Semi-Magic. International Journal of Mathematical Education in Science and Technology, 32, 624-629.
  5. TRENKLER, G. (1994). Singular Magic Squres. International International Journal of Mathematical Education in Science and Technology, 25, 595-597.