A Necessary and Sufficient Condition Satisfied by Decomposable Elements in Completely Symmetrical Tensor Spaces

数学季刊 ›› 1994, Vol. 9 ›› Issue (4): 52-60.

A Necessary and Sufficient Condition Satisfied by Decomposable Elements in Completely Symmetrical Tensor Spaces

Jiangsu Educational Institute,Nanjing,210013

收稿日期:1993-05-08 出版日期:1994-12-30 发布日期:2025-04-09

A Necessary and Sufficient Condition Satisfied by Decomposable Elements in Completely Symmetrical Tensor Spaces

Jiangsu Educational Institute,Nanjing,210013

Received:1993-05-08 Online:1994-12-30 Published:2025-04-09

摘要/Abstract

摘要： In this paper,using the parameter method the author reduces the problem of the necessary and sufficient condition of decomposable elements in V'm)to the problem of decomposability of completely sym- metrical tensors of type I and type I,by means of the equivalence transformation of decomposability of completely symmetrical tensors.It shows that the generated matrix of decomposable elements is obtained by the row elementary transformation,a necessary and sufficient condition that the type I and I of completely symmetrical tensors are decomposable elements is also obtained.

关键词: , generated polynomial, generated matrix, the completely symmetrical tensors of type I and type I

Abstract: In this paper,using the parameter method the author reduces the problem of the necessary and sufficient condition of decomposable elements in V'm)to the problem of decomposability of completely sym- metrical tensors of type I and type I,by means of the equivalence transformation of decomposability of completely symmetrical tensors.It shows that the generated matrix of decomposable elements is obtained by the row elementary transformation,a necessary and sufficient condition that the type I and I of completely symmetrical tensors are decomposable elements is also obtained.

Key words: , generated polynomial, generated matrix, the completely symmetrical tensors of type I and type I

中图分类号:

O241

朱忠南. A Necessary and Sufficient Condition Satisfied by Decomposable Elements in Completely Symmetrical Tensor Spaces[J]. 数学季刊, 1994, 9(4): 52-60.

Zhu Zhongnan. A Necessary and Sufficient Condition Satisfied by Decomposable Elements in Completely Symmetrical Tensor Spaces[J]. Chinese Quarterly Journal of Mathematics, 1994, 9(4): 52-60.

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A Necessary and Sufficient Condition Satisfied by Decomposable Elements in Completely Symmetrical Tensor Spaces

A Necessary and Sufficient Condition Satisfied by Decomposable Elements in Completely Symmetrical Tensor Spaces

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