منابع مشابه
Invertible and Nilpotent Matrices over Antirings
Abstract. In this paper we characterize invertible matrices over an arbitrary commutative antiring S with 1 and find the structure of GLn(S). We find the number of nilpotent matrices over an entire commutative finite antiring. We prove that every nilpotent n×n matrix over an entire antiring can be written as a sum of ⌈log2 n⌉ square-zero matrices and also find the necessary number of square-zer...
متن کاملOn nilpotency of matrices over antirings
Article history: Received 13 May 2010 Accepted 1 June 2010 Available online 4 July 2010 Submitted by R.A. Brualdi AMS classification: 15A15 15A18
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Let the columns of a p× q matrix M over any ring be partitioned into n blocks, M = [M1, . . . , Mn]. If no p × p submatrix of M with columns from distinct blocks Mi is invertible, then there is an invertible p×p matrix Q and a positive integer m ≤ p such that QM = [QM1, . . . , QMn] is in reduced echelon form and in all but at most m − 1 blocks QMi the last m entries of each column are either a...
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We propose a generalization of the graphical chip-firing model allowing for the redistribution dynamics to be governed by any invertible integer matrix while maintaining the long term critical, superstable, and energy minimizing behavior of the classical model.
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A square matrix is said to be alternating-clean if it is the sum of an alternating matrix and an invertible matrix. In this paper, we determine all alternating-clean matrices over any division ring K. If K is not commutative, all matrices are alternating-clean, with the exception of the 1× 1 zero matrix. If K is commutative, all matrices are alternating-clean, with the exception of odd-size alt...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.01.018