科研之友
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摘要
Let A(i,) i = 1,..., m, be n x n positive definite matrices whose diagonal blocks are n(j) -square matrices A(i)((j)) , j = 1,...,k. Choi recently proved det (Sigma(m)(i=1)A(i)(-1)) >= det (Sigma(m)(i=1)(A(i)((1)))(-1)) ...det (Sigma(m)(i=1)(A(i)((k)))(-1)). We first give a new proof of this inequality, and then present an analogous inequality involving the Hadamard product det (Pi(m)(i=1)omicron A(i)(-1)) >= det (Pi(m)(i=1)omicron(A(i)((1)))(-1))...det (Pi(m)(i=1)omicron(A(i)((k)))(-1)).
