Shi Tong-ye
Abstract
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.
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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.
Key concepts: Positive-definite matrix, Mathematics, Symmetric matrix, Diagonal matrix, Matrix (chemical analysis), Diagonal, Combinatorics, Constant (computer programming)