科研之友
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摘要
In this note, we prove that if A(1),..., A(m) are nxn contractivematrices and p1,..., pm > 0 with 1 p1 + 1 p2 + ... + 1 pm =1, then k Pi j=1 (1 -.j(vertical bar A1 ... Am vertical bar) r >= m Pi i=1 k Pi j=1 1 -.j(vertical bar Ai vertical bar) rpi/1 pi for each k =1, 2,..., n. This generalizes an inequality given by Marcus in 1958.
