关键词: Jordan, 平方根矩阵, 广义逆.

Abstract:

J=J_m1(λ₁)⊕J_m2(λ₂) is the Jordan normal form which has two Jordan blocks J_m1(λ₁) and J_m2(λ₂).J has square-rooting matrices iff one of following holds:

(i) λ₁,λ₂≠0;

(ii)λ₁=0, but λ₂≠0, then m₁=1, or λ₁≠0, but λ₂=0, then m₂=1;

(iii) λ₁=λ₂=0, then m₁=m₂,m₁+1=m₂ or m₂+1=m₁.And we give the expresses of square-rooting matices of J.

Key words: Jordan block, square-rooting matrix, generatized inverse matrix.