e Sistemleri
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Date
1990
Authors
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Publisher
Uludağ Üniversitesi
Abstract
Bu çalışmada Tensör Analiz de karşılaşılan kontravaryant ve kovaryant e sistemleri n boyutlu uzayda incelendi. Önce tanımlar verilerek e sistemleri yardımıyla kronecker deltanın tanımı yapıldı. Kronecker deltanın özelliğinden yararlanarak e; 1 ... N i 1 ···N çarpımının terim sayısı formülIeştirildi ve determinantlara uygulanışı gösterildi. Bu uygulamadan faydalanarak, e' 1 ···'N sembolünün + 1 ağırlığında, ''···'N sembolünün -1 ağırlığında relatif tensörler oldukları, permütasyonların özelliklerinden yararlanarak farklı iki yol izlenerek verildi.
In this study, contravariant and covariant e-systems which are met in tensor analysis are investigated in then dimensional space. Firstly, kronecker delta is defined by the help of e-systems which are found out by previous definitions. The number of tems appearing in the sum of e;1···N· e'1···'N multiplication is formülated by taking into consideration the characteristics of kronecker delta. Later on, it is shown the applications of it to the determinants. lt is known that the permutations symbols e i · · ·1 N and e i .. . N are relative tensors of weights + 1 and -1, respective/y-: · It has been given to be the same tensors following, different ways by use particularly of permutations.
In this study, contravariant and covariant e-systems which are met in tensor analysis are investigated in then dimensional space. Firstly, kronecker delta is defined by the help of e-systems which are found out by previous definitions. The number of tems appearing in the sum of e;1···N· e'1···'N multiplication is formülated by taking into consideration the characteristics of kronecker delta. Later on, it is shown the applications of it to the determinants. lt is known that the permutations symbols e i · · ·1 N and e i .. . N are relative tensors of weights + 1 and -1, respective/y-: · It has been given to be the same tensors following, different ways by use particularly of permutations.
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Keywords
e Sistem, Tensör analiz, Kontravaryant, Kovaryant, Delta, e System, Tensor analysis, Contravariant, Covariant
Citation
Akyüz, İ. (1990). ''e Sistem''. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 5(2), 23-27.