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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 authors considered the ring of square matrices of order m over a projective free ring R with involution such that R m is a module of finite length, providing a new characterization for range-Hermitian matrices over the complexes.
52 citations
TL;DR: In this paper, a new estimation method for the factor loading matrix in generalized orthogonal GARCH (GO-GARCH) models is proposed, based on the eigenvectors of a suitably defined sample autocorrelation matrix of squares and cross-products of the process.
52 citations
TL;DR: A necessary and sufficient condition for a linear system of equations over a fuzzy algebra to have a unique solution is formulated and the equivalence of strong regularity and trapezoidal property is proved.
52 citations
TL;DR: In this article, a new proof for the inequality tr (XY) \leq \parallel X ∈ {2} \cdot tr Y under the condition that X may be any square matrix.
Abstract: A new proof is presented for the inequality, tr (XY) \leq \parallel X \parallel_{2} \cdot tr Y . This argument is valid under the condition that Y be real symmetric nonnegative definite; X may be any square matrix.
52 citations
TL;DR: In this article, the stability of a sampled-data system with sampling interval lengths selected from a finite set of matrices is studied, and conditions for stabilizability involving pre-contractiveness, contractiveness and positive definiteness are given.
Abstract: A sampled-data system with sampling interval lengths selected from a finite set is considered. Stabilizability of the system via feedbacks associated with sampling interval lengths is studied, and conditions for stabilizability involving “pre-contractiveness”, “contractiveness” and “positive definiteness” of a finite set of matrices are given. Included in these results is a generalization of a theorem by P. Stein stating that for a real square matrix H, $\lim _{n \to \infty } H^n = 0$ if and only if there is a symmetric matrix Q such that $Q - H^T QH$ is positive definite. Finally, some results concerning a choice of feedbacks which will produce stability are presented.
52 citations