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In this paper, some natures of Frobenius norm are obtained by using majorization, which can be used in numerical mathematics and matrix perturbation analysis.
In this paper, we define an online algorithm to learn the generalized cosine similarity measures for k-NN classification and hence a similarity matrix A corresponding to a bilinear form. In contrary to the standard cosine measure, the normalization is itself dependent on the similarity matrix which makes it impossible to use directly the algorithms developed for learning Mahanalobis distances, based...
In this paper, consensus problems of a multi-agent directed network with nonlinear perturbations is considered. When the consensus of a directed network may be destroyed by the unknown perturbations, the impulsive control is introduced to ensure the consensus of all nodes. Then, based on a transformation of matrix theory, the original impulsive system is turned into a reduced-order impulsive system,...
In this note, we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A-ghT, and where one of the matrices is singular. A necessary and sufficient condition for the existence of such a function is given in terms of the spectrum of...
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