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Linear spanning sets for matrix spaces

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Author Micheli Giacomo, Rosenthal Joachim, Vettori Paolo, Micheli Giacomo, Rosenthal Joachim, Vettori Paolo,
Project Algebraic Constructions and Decoding of Subspace Codes
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Original article (peer-reviewed)

Journal Linear Algebra and its Applications
Volume (Issue) 483
Page(s) 309 - 322
Title of proceedings Linear Algebra and its Applications
DOI 10.1016/j.laa.2015.06.008

Open Access

Abstract

Necessary and sufficient conditions are given on matrices A, B and S, having entries in some field F and suitable dimensions, such that the linear span of the terms A^i S B^j over F is equal to the whole matrix space. This result is then used to determine the cardinality of subsets of F[A] S F[B] when F is a finite field.
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