设SC_n(Q)表示所有n×n的四元数自共轭矩阵的集合。当A∈SC_n(Q)时,λ_s(A)为A的特征值且满足λ_1(A)≥λ_2(A)≥…≥λ_n(A)。本文证明了 1)如果A∈SC_n(Q), P∈Q^(n×n) ,则 sum from s=1 to k(λ_(n-s-1)(PAP^n))≤sum from ...设SC_n(Q)表示所有n×n的四元数自共轭矩阵的集合。当A∈SC_n(Q)时,λ_s(A)为A的特征值且满足λ_1(A)≥λ_2(A)≥…≥λ_n(A)。本文证明了 1)如果A∈SC_n(Q), P∈Q^(n×n) ,则 sum from s=1 to k(λ_(n-s-1)(PAP^n))≤sum from s=1 to k(λ_s(A)λ_s(PP^n)), k=1,2,...,n; sum from s=1 to k(λ_(n-s+1)(A)λ_s(PP^n))≤sum from s=1 to k(λ_s(PAP^n)), 2) 如果A,B,C∈SC_n(Q)且B=C-A, 则sum from s=1 to k(λ_s^2(B))≥sum from s=1 to k ([λ_s(C)-λ_s(A)]~2).展开更多
文摘设SC_n(Q)表示所有n×n的四元数自共轭矩阵的集合。当A∈SC_n(Q)时,λ_s(A)为A的特征值且满足λ_1(A)≥λ_2(A)≥…≥λ_n(A)。本文证明了 1)如果A∈SC_n(Q), P∈Q^(n×n) ,则 sum from s=1 to k(λ_(n-s-1)(PAP^n))≤sum from s=1 to k(λ_s(A)λ_s(PP^n)), k=1,2,...,n; sum from s=1 to k(λ_(n-s+1)(A)λ_s(PP^n))≤sum from s=1 to k(λ_s(PAP^n)), 2) 如果A,B,C∈SC_n(Q)且B=C-A, 则sum from s=1 to k(λ_s^2(B))≥sum from s=1 to k ([λ_s(C)-λ_s(A)]~2).
