Article ID Journal Published Year Pages File Type
4601979 Linear Algebra and its Applications 2010 8 Pages PDF
Abstract

Letf(x1,…,xn)=∑i,j=1nαijxixj,aij=aji∈Rbe a real quadratic form such that the trace of the Hermitian matrixf(V1,…,Vn):=∑i,j=1nαijVi∗Vjis nonnegative for all unitary 2n×2n2n×2n matrices V1,…,VnV1,…,Vn. We prove that f(U1,…,Un)f(U1,…,Un) is positive semidefinite for all unitary matrices U1,…,UnU1,…,Un of arbitrary size m×mm×m.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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