Nonnegative matrices, max-algebra and applications
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منابع مشابه
On Some Properties of the Max Algebra System Over Tensors
Recently we generalized the max algebra system to the class of nonnegative tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and i...
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In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
متن کاملOn Commuting Matrices in Max Algebra and in Classical Nonnegative Algebra
This paper studies commuting matrices in max algebra and nonnegative linear algebra. Our starting point is the existence of a common eigenvector, which directly leads to max analogues of some classical results for complex matrices. We also investigate Frobenius normal forms of commuting matrices, particularly when the Perron roots of the components are distinct. For the case of max algebra, we ...
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Max-times algebra, sometimes known as subtropical algebra, is a semi-ring over the nonnegative real numbers where the addition operation is the max function and the multiplication is the standard one. Factorizing a nonnegative matrix over the maxtimes algebra, instead of the standard (nonnegative) one, allows us to find structures and regularities that cannot be easily expressed in the standard...
متن کاملOn visualization scaling, subeigenvectors and Kleene stars in max algebra
The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix theory, are strongly related to max algebra. One problem is that of strict visualization scaling, defined as, for a given nonnegative matrix A, a diagonal matrix X such that all elements of X −1 AX are less than or equal...
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