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Rank of convex combinations of matrices

Ранг выпуклых комбинаций матриц

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Reliable Computing

Abstract

LetA andB be complex rectangular matrices of the same rankr. We characterize the property that all convex combinations ofA andB are of rankr. Moreover, forA andB of full rank, some conditions for the matrix setr(A, B) (c(A, B), resp.) whose rows (columns, resp.) are independent convex combinations of the rows (columns, resp.) ofA andB are also proposed.

Abstract

ПустьА иВ — комплексые прямоугольные матрипы одного и того же рангаr. Докаэывается, что все выпуклые комбинацииА иВ также имеют рангr. Кроме того, для матрицА иВ полного ранга выводятся некоторые свойства множества матрицr(А, В) (и, соответственно,с(А, В)), чьи строки (или столбцы) являются неэависимыми выпуклыми комбинациями строк (или столбцов) матрицА иВ.

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References

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769, Poznań, Poland

    Tomasz Szulc

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  1. Tomasz Szulc
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© T. Szulc, 1996

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Szulc, T. Rank of convex combinations of matrices. Reliable Comput 2, 181–185 (1996). https://doi.org/10.1007/BF02425922

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  • DOI: https://doi.org/10.1007/BF02425922

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