一个Jordan 块的平方根矩阵

Abstract

Abstract:

in this paper ,we give that a jordan block J_{m^{(λ) has square -rooting matrices if and only if m=11 or λ≠0,}}J_{m^{(λ) has exactly two square-rooting matrices:}}：±A，where a₁ = c , a₂ = 1/2c , a₃= -1/8c³ ,… ,

_{^{ak = -(a2ak-1+a3ak-2+…+ak-2a3+ak-1a2)/2a1 ,… (k=3,4,…,m), c2 = λ.}}

Key words: 　Ｓｑｕａｒｅｒｏｏｔｉｎｇｍａｔｒｉｘ, Ｊｏｒｄａｎｂｌｏｃｋ, Ｅｉｇｅｎｖａｌｕｅ, Ｏｒｄｅｒ．

CLC Number:

１５Ａ

Zhu Degao. On Square-Rooting Matrices of A Jordan Block[J].Acta mathematica scientia,Series A, 1999, 19(3): 318-321.

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On Square-Rooting Matrices of A Jordan Block

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