Topic
Square matrix
About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.
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TL;DR: In this paper, it was shown that every real matrix contained in a matrix interval is sign-regular if and only if two special matrices taken from that matrix interval are sign regular.
27 citations
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26 May 2013TL;DR: It is shown that bilinear inverse problems can be posed as rank-1 matrix recovery problems subject to linear constraints and sufficient conditions for identifiability are developed for the cases when rank-2 matrices are present in the null space of the linear operator.
Abstract: This paper considers identifiability and recoverability in bilinear inverse problems which is relevant to blind deconvolution and matrix factorization It is shown that bilinear inverse problems can be posed as rank-1 matrix recovery problems subject to linear constraints Sufficient conditions for identifiability are developed for the cases when rank-2 matrices are present in the null space of the linear operator Signal recovery using the nuclear norm heuristic for rank-1 matrix recovery is considered and simple conditions for success are provided
27 citations
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TL;DR: In this article, an algorithm for the reconstruction of a symmetric matrix from the spectral data is given, and all cases in which the number of solutions is finite are determined, and the results are applied to a certain inverse eigenvalue problem which arises in molecular spectroscopy.
27 citations
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TL;DR: An operator calculus is developed, where the key step is manipulation of analytic functions f(z) extended to matrix arguments extended to Matrix arguments for matrix-exponential distributions.
Abstract: A distribution G on [math not displayed] is called matrix-exponential if the density has the form αeTz s where α is a row vector, T a square matrix and s a column vector. Equivalently, the Laplace transform is rational. For such distributions, we develop an operator calculus, where the key step is manipulation of analytic functions f(z) extended to matrix arguments. The technique is illustrated via an inventory model moving according to a reflected Brownian motion with negative drift, such that an order of size Q is placed when the stock process down-crosses some level q. Explicit formulas for the stationary density are found under the assumption that the leadtime Z has a matrix-exponential distribution, and involve expressions of the form f(T) where [math not displayed].
27 citations
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06 Feb 2009TL;DR: In this article, an apparatus and method for transmitting a signal in a communication system using a hybrid automatic repeat re-quest (HARQ) scheme are provided, which includes generating a codeword vector by encoding an information vector by using a first parity check matrix of Low Density Parity Check (LDPC) codes, generating a transmission vector by processing the codewords vector, and transmitting the transmission vector.
Abstract: An apparatus and method for transmitting a signal in a communication system using a Hybrid Automatic Repeat reQuest (HARQ) scheme are provided. The method includes generating a codeword vector by encoding an information vector by using a first parity check matrix of Low Density Parity Check (LDPC) codes, generating a transmission vector by processing the codeword vector, and transmitting the transmission vector. When the first parity check matrix includes a plurality of square matrix columns, each square matrix includes a size of L×L, the first parity check matrix is one of p parity check matrixes stored in the signal transmission apparatus, the p parity check matrixes support different numbers of information vector square matrix columns, and each of the numbers of information vector square matrix columns indicates the number of square matrix columns corresponding to the information vector from among the plurality of square matrix columns. The first parity check matrix is a parity check matrix supporting the number of information vector square matrix columns determined by using the length of the information vector and the value L from the p parity check matrixes, and the value L is determined by using p and the length of the information vector.
27 citations