Solving Linear Systems over Additively Idempotent Semirings: Characterization of Maximal Solutions and Computational Complexity
The core message of this article is to provide a complete characterization of the maximal solution of linear systems over additively idempotent semirings, and to analyze the computational complexity of solving such systems, particularly in the case of generalized tropical semirings.
Characterization of Matrices Satisfying the Reverse Order Law for the Moore-Penrose Pseudoinverse
The core message of this article is to provide a constructive characterization of matrices satisfying the reverse order law for the Moore-Penrose pseudoinverse. The authors show that any matrix satisfying this law can be obtained through a specific construction involving the right singular vectors of the given matrix.
Analyzing Maximally Extendable Sheaf Codes in Linear Algebra
The authors introduce the concept of maximally extendable sheaf codes, demonstrating their significance in linear algebra and coding theory.
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