Notes on the Sum-Rank Weight of a Matrix with Restricted Rank
Hugo Sauerbier Couv\'ee, Hedongliang Liu
TL;DR
This paper investigates the sum-rank weight of matrices with restricted rank, providing formulas and bounds for the probability that such matrices achieve maximum sum-rank weight based on their rank and block structure.
Contribution
It introduces new formulas and lower bounds for the sum-rank weight of matrices with restricted rank, enhancing understanding of their probabilistic properties.
Findings
Derived a formula for the sum-rank weight of matrices
Established lower bounds on the probability of maximum sum-rank weight
Analyzed the relationship between matrix rank and sum-rank weight
Abstract
These notes cover a few calculations regarding the sum-rank weight of a matrix in relation to its rank. In particular, a formula and lower bounds are given on the probability that a matrix of rank consisting of blocks has sum-rank weight .
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Taxonomy
Topicsgraph theory and CDMA systems · Matrix Theory and Algorithms · Tensor decomposition and applications