Mn(C)中的不可约性(英文)

Irreducibility in Mn(C)

中文关键词:  不可约性  正交投影  谱

英文关键词:irreducibility  orthogonal projection  spectrum

中文摘要:

      对于M_n(C)(所有n×n矩阵的全体)中的不可约矩阵得到以下结果:对于任意A∈M_n(C),设λ₁, λ₂,…,λ_m为A的所有特征值,这里m≤n而且当i≠j时,λ_i≠λ_j.则A是不可约的当且仅当任意P∈A′(A),P^*=P=P²,有σ(P|ker(A-λ₁))=σ(P|ker(A-λ₂))=…=σ(P|ker(A-λ_m))为单点集.

英文摘要:

      In this paper, we investigate the irreducibility of the n×n complex matrix and obtain the following result: For each A in M_n(C), let λ₁, λ₂,…,λ_m be all eigenvalues of A, where m≤n and λ_i≠λ_j if i≠j. Then A is irreducible if and only if for each P in A′ (A) and P^* = P = P²,we have σ(P|ker(A - λ₁)) =σ(P|ker(A - λ₂)) = …= σ(P|ker(A - λ_m)) = singleton.