行随机矩阵的逆特征值问题

非负矩阵逆特征值问题的理论价值和应用背景一直吸引不少学者从事于这个热门课题的研究.论文研究行随机矩阵逆特征值问题,考虑一类特殊的复数集Λ=∪k=1mΛk,m>0,每个Λk含有pk>0个元,其中一元是λk1>0,其余元是ωke2πi/pk,…,ωke2(pk-1)πi/pk,0<ωk≤λk1.论文同时给出了求解的方法.当p1,…,pm全为2时,Λ变成2m+1非零个实数的集合.论文同时也给出以已知任意奇数个非零实数为谱的行随机矩阵逆特征值问题有解的充分条件及求解的方法.

Row random inverse eigenvalue problem

We proved the sufficient conditions for the existence of a row random matrix with a given spectrum Λ=∪k=1 mΛk,m>0,where each Λkhas pk>0 elements among which one was λk1>0 and the others were ωe2πi/pk,ωe4πi/pk,…,ωe2(pk-1)πi/pk with 0<ω≤λk1.We also gave the method to construct the solution matrix.In the case when p1,…,pm were all equal to 2,Λ became a list of 2m+1 real numbers for any positive integer m and our result gave sufficient conditions for a list of 2m+1 real numbers to be realizable by a row random matrix.