Topic
Square matrix
About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: The local eigenvalue statistic, arising in a certain neighborhood of the edges of the support of the Density of States, is independent of the form of the potential, determining the matrix model as discussed by the authors.
Abstract: Basing on our recent results on the $1/n$-expansion in unitary invariant random matrix ensembles, known as matrix models, we prove that the local eigenvalue statistic, arising in a certain neighborhood of the edges of the support of the Density of States, is independent of the form of the potential, determining the matrix model Our proof is applicable to the case of real analytic potentials and of supports, consisting of one or two disjoint intervals
37 citations
[...]
TL;DR: In this paper, a weak group inverse (WG inverse) was introduced for square matrices of an arbitrary index, and some of its characterizations and properties were derived. And the core-EP order was derived by using the WG inverses.
Abstract: In this paper, we introduce a weak group inverse (called the WG inverse in the present paper) for square matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order and the other is a partial order, and derive several characterizations of the two orders. At last, one characterization of the core-EP order is derived by using the WG inverses.
37 citations
Patent•
02 Jul 1997TL;DR: In this article, a method and apparatus for converting frequency-coefficient matrices between a configuration in which the matrices are transforms of unoverlapped image-data matrices and a configuration where the matrixrices are transformations of overlapped image data matrices, the image data terms corresponding to pixels from an original image, is described.
Abstract: A method and apparatus are disclosed for converting frequency-coefficient matrices between a configuration in which the matrices are transforms of unoverlapped image-data matrices and a configuration in which the matrices are transforms of overlapped image-data matrices, the image-data matrices comprising image-data terms corresponding to pixels from an original image, the method comprising the steps of: deriving a conversion matrix; transposing the conversion matrix; matrix multiplying a first frequency-coefficient matrix of one configuration by the conversion matrix; matrix multiplying a second frequency-coefficient matrix of the same configuration by the transpose conversion matrix; and combining the product results to form a matrix formatted in the other configuration.
37 citations
TL;DR: In this paper, three types of predictors for factor scores are available: linear, linear conditionally unbiased, and linear correlation preserving, and each of these constraints generates a class of predictor, which are defined in terms of Lowner's partial matrix order applied to matrices of mean square error of prediction.
Abstract: From the literature three types of predictors for factor scores are available These are characterized by the constraints: linear, linear conditionally unbiased, and linear correlation preserving Each of these constraints generates a class of predictors Best predictors are defined in terms of Lowner's partial matrix order applied to matrices of mean square error of prediction It is shown that within the first two classes a best predictor exists and that it does not exist in the third
37 citations
TL;DR: Li et al. as mentioned in this paper proposed a higher-order convergent iterative method to compute the generalized inverse of a given matrix by using the displacement theory, which can be used to compute generalized inverse A T, S (2 ) of Toeplitz matrices.
37 citations