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

Yıl 2003, Cilt: 2 Sayı: 2, 7 - 15, 17.08.2003

Fikri Akdeniz , Asuman Türkmen

Öz

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

Anahtar Kelimeler

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

Sihirli Kare Matrislerin Öz Değerlerinin İncelenmesi ve Moore-Penrose İnversi

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• BOOTH, A. D. and BOOTH, K.H.V. (1955). On magic Squares. The Mathematical Gazette, 39, 132-133.
• 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.
• RAO, C. R. and MITRA, S. K. (1971). Generalized Inverse of Matrices and Its Applications, New York: John Wiley.
• 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.