J4 ›› 2011, Vol. 49 ›› Issue (03): 465-470.
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YANG Dinghua
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Abstract:
Using the theory and method of distance geometry, we proved that a necessary and sufficient condition for Σ(A,N+1) being on an (n-1)dimensional hypersphere is that the matrix M(Σ(A,N+1))=(a2kl)(k,l=0,1,…,N) has rank n+1, where M(Σ(A,N+1)) is the distance square matrix of Σ(A,N+1), Σ(A,N+1)={A0,A1,…,AN} is an ndimensional finite set of points in ndimensional Euclidean space. A necessary and sufficient condition for 5 points on a 2dimensional hypersphere was given.
Key words: ndimensional Euclidean space, (n-1)dimensional , hypersphere, distance square matrix, rank
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YANG Ding-Hua. A Necessary and Sufficient Condition fora Finite Set of Points on a HyperSphere[J].J4, 2011, 49(03): 465-470.
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http://xuebao.jlu.edu.cn/lxb/EN/Y2011/V49/I03/465
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