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《Studies in College Mathematics》 2012-06
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A Limit Related to Real Symmetric Positive Definite Matrix

SHI Tongye,Deng Jiekun (Pukou Institute,Naval Command College,Nanjing 211800,PRC)  
By using the property that real symmetric positive definite matrix is orthogonally similar to diagonal matrix and the squeezing theorem,we prove that if Ai∈R l×l is a real symmetric positive definite matrix,Xi∈R l,Xi■R(Ai-ρ(Ai)I),ci0(i=1,2,…,m),k is a nonnegative constant,then limn→∞n∑mi=1ci(XTiAniXi)k=max1≤i≤m[ρ(Ai)]k.
【CateGory Index】: O151.21
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【Co-citations】
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