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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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Journal ArticleDOI
TL;DR: The decomposition of fuzzy matrices is closely related to fuzzy databases and fuzzy retrieval models and some properties of decomposition are shown.
Abstract: A problem of decomposition of fuzzy rectangular matrices is examined and some properties of decomposition are shown. Any fuzzy matrix can be factored into a product of a square matrix and a rectangular matrix of the same dimension. This square matrix has reflexivity and transitivity. The decomposition of fuzzy matrices is closely related to fuzzy databases and fuzzy retrieval models.

24 citations

Journal ArticleDOI
TL;DR: An efficient algorithm for checking the@l-robustness and strong @l-Robustness of a given matrix is introduced and a characterization of @l -robust and strongly @l.robust matrices is presented.

24 citations

Journal ArticleDOI
TL;DR: In this article, the problem of solving the linear system A x ǫ = b, where A is the coefficient matrix, b is the known right hand side vector and x is the solution vector to be determined, is considered.

24 citations

Journal ArticleDOI
TL;DR: It is shown that the elementwise convergence to zero of the discounted deviations from the stable age structure is complete and exponential and the sum, over all time, of the signed discounted deviations may be easily calculated from a fundamental matrix based on the projection matrix.
Abstract: In a closed, unisexual, age-structured population with age-specific birth and death rates which are constant in time, the vector describing a census by age categories will, as time increases, approach proportionality to the stable age structure implied by the vital rates. This stable age structure is the dominant eigenvector of a demographic projection matrix which carries out the action on a census vector of the age-specific vital rates. We show that the elementwise convergence to zero of the discounted deviations from the stable age structure is complete and exponential. The sum, over all time, of the signed discounted deviations may be easily calculated from a fundamental matrix based on the projection matrix. These results are proved for any primitive nonnegative square matrix. In the demographic context, these results suggest alternatives to an index which has been used to measure the distance from an observed to a stable age structure.

24 citations

Proceedings ArticleDOI
06 Jul 2016
TL;DR: If the state matrix is diagonal and the control input matrix is a node-link incidence matrix, the open-loop system's property of internal positivity is preserved by the control law.
Abstract: We address H∞ state feedback and give a simple form for an optimal control law applicable to linear time invariant systems with symmetric and Hurwitz state matrix. More specifically, the control law as well as the minimal value of the norm can be expressed in the matrices of the system's state space representation, given separate cost on state and control input. Thus, the control law is transparent, easy to synthesize and scalable. If the plant possesses a compatible sparsity pattern, it is also distributed. Examples of such sparsity patterns are included. Furthermore, if the state matrix is diagonal and the control input matrix is a node-link incidence matrix, the open-loop system's property of internal positivity is preserved by the control law. Finally, we give an extension of the optimal control law that incorporate coordination among subsystems. Examples demonstrate the simplicity in synthesis and performance of the optimal control law.

24 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202322
202244
2021115
2020149
2019134
2018145