一类特殊矩阵的特征值

本文利用矩阵A =αβT 的特征值, 对与矩阵k1 I + k2αβT 的特征值相关的一些典型题     

矩阵的初等变换法求特征值及特征向量

利用矩阵的行初等变换法及分块矩阵理论，给出了矩阵的特征值及特征向量的简易求法。     

代数特征问题的一个注记

改进了求代数特征值与特征向量的传统方法,给出了一种用初等变换来求代数特征值与特征向量的方法.     

对称变换的和的非零特征根所对应的特征子空间的正交性

讨论了欧氏空间中的两个实对称变换的非零特征根的所对应特征子空间互相正交的充要条件，并用比较简捷的方法证明了定理1，将它应用到概率论中证明了Craig定理。     

Principal component analysis using neural network

The authors present their analysis of the differential equation dX(t)/dt=AX(t)-XT(t)BX(t)X(t), where A is an unsymmetrical real matrix, B is a positive definite symmetric real matrix, X∈Rn; showing that the equation characterizes a class of continuous type full-feedback artificial neural network; We give the analytic expression of the solution; discuss its asymptotic behavior; and finally present the result showing that, in almost all cases, one and only one of following cases is true. 1. For any initial value X0∈Rn, the solution approximates asymptotically to zero vector. In this case, the real part of each eigenvalue of A is non-positive. 2. For any initial value X0 outside a proper subspace of Rn, the solution approximates asymptotically to a nontrivial constant vector (X0). In this case, the eigenvalue of A with maximal real part is the positive number λ=‖(X0)‖2B and (X0) is the corresponding eigenvector. 3. For any initial value X0 outside a proper subspace of Rn, the solution approximates asymptotically to a non-constant periodic function (X0,t). Then the eigenvalues of A with maximal real part is a pair of conjugate complex numbers which can be computed.     

线性主动结构动力学属性的基础性研究

通过线性主动结构动力学属性的基础性研究,归纳了主动结构动力学的主要问题,运用特征向量对主动结构进行了特征问题分析,得到了线性主动结构模态的基本属性,通过对主动梁的研究,验证了所得结论的正确性。     

Drivers of spin-off performance in industry clusters: Embodied knowledge or embedded firms?

Numerous studies attest to the distinctive performance of intra-industry spin-offs located in agglomerated regions. Besides entrepreneurs’ pre-entry experience, both superior hires and regional embeddedness have been suggested as factors contributing to this pattern. We employ linked employer-employee data to assess their relevance in the empirical context of the Portuguese plastic injection molds industry. We find that the longevity of entrants is associated with the number and quality of early employees hired from within the industry, consistent with the importance of embodied knowledge flows. Our findings do not suggest that entrants’ centrality in the regional industry network enhances their longevity.     

Within-journal self-citations and the Pinski-Narin influence weights

The Journal Impact Factor (JIF) is linearly sensitive to self-citations because each self-citation adds to the numerator, whereas the denominator is not affected. Pinski and Narin (1976) Influence Weights (IW) are not or marginally sensitive to these outliers on the main diagonal of a citation matrix and thus provide an alternative to JIFs. Whereas the JIFs are based on raw citation counts normalized by the number of publications in the previous two years, IWs are based on the eigenvectors in the matrix of aggregated journal-journal citations without a reference to size: the cited and citing sides are normalized and combined by a matrix approach. Upon normalization, IWs emerge as a vector; after recursive multiplication of the normalized matrix, IWs can be considered a network measure of prestige among the journals in the (sub)graph under study. As a consequence, the self-citations are integrated at the field level and no longer disturb the analysis as outliers. In our opinion, this independence of the diagonal values is a very desirable property of a measure of quality or impact. As an example, we elaborate Price’s (1981b) matrix of aggregated citation among eight biochemistry journals in 1977. Routines for the computation of IWs are made available at http://www.leydesdorff.net/iw.