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

Year 2003, Volume: 2 Issue: 2, 7 - 15, 17.08.2003

Fikri Akdeniz Asuman Türkmen

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

Keywords

Eigenvalue, Magic Constant, Magic Square, Moore- Penrose Inverse, Semi-Magic Square

Sihirli Kare Matrislerin Öz Değerlerinin İncelenmesi ve Moore-Penrose İnversi

Abstract

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.

Keywords

Moore-Penrose Inversi, Öz Değer, Sihirli Kare, Sihirli Sabit, Yarı-Sihirli Kare

References

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• 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.
• TRENKLER, G. (1994). Singular Magic Squres. International International Journal of Mathematical Education in Science and Technology, 25, 595-597.