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, the Perron-Frobenius theory is extended to the 2D case and conditions are provided guaranteeing the existence of a common maximal eigenvector for two nonnegative matrices with irreducible sum.
34 citations
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TL;DR: A tensor framework to solve the problem of nonunitary joint block diagonalization (JBD) of a set of real or complex valued matrices and shows that exact JBD can be computed by a closed-form solution based on eigenvalue analysis.
Abstract: This paper introduces a tensor framework to solve the problem of nonunitary joint block diagonalization (JBD) of a set of real or complex valued matrices We show that JBD can be seen as a particular case of the block-component-decomposition (BCD) of a third-order tensor The resulting tensor model fitting problem does not require the block-diagonalizer to be a square matrix: the over- and underdetermined cases can be handled To compute the tensor decomposition, we build an efficient nonlinear conjugate gradient (NCG) algorithm In the over- and exactly determined cases, we show that exact JBD can be computed by a closed-form solution based on eigenvalue analysis In approximate JBD problems, this solution can be used to efficiently initialize any iterative JBD algorithm such as NCG Finally, we illustrate the performance of our technique in the context of independent subspace analysis (ISA) based on second-order statistics (SOS)
34 citations
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TL;DR: In this article, a representation for the Drazin inverse of an arbitrary square matrix in terms of the eigenprojection is established, and the Laurent expansion of the resolvent of the matrix has coefficients (for the nonnegative indices) which are powers of the Dazin inverse.
Abstract: A representation for the Drazin inverse of an arbitrary square matrix in terms of the eigenprojection is established in this paper. The Laurent expansion of the resolvent of our matrix has coefficients (for the nonnegative indices) which are powers of the Drazin inverse. Using this expansion we immediately get some limit theorems concerning the index of the given matrix. The results hold for matrices over a topological Hausdorf field.
34 citations
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TL;DR: In this paper, the spectral radius of the Jacobi matrix of a square H-matrix and the generalized diagonal dominance property of the comparison matrix were used to characterize the set of general H -matrices with singular or nonsingular comparison matrices.
34 citations
01 Jan 2016
TL;DR: Thank you very much for reading jacobians of matrix transformations and functions of matrix argument, which people have look hundreds of times for, but end up in harmful downloads.
Abstract: Thank you very much for reading jacobians of matrix transformations and functions of matrix argument. As you may know, people have look hundreds times for their favorite readings like this jacobians of matrix transformations and functions of matrix argument, but end up in harmful downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they juggled with some malicious bugs inside their laptop.
34 citations