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Convex Sets of Full Rank Matrices

In: Developments in Reliable Computing

Author

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  • Barbara Kołodziejczak

    (Adam Mickiewicz University, Faculty of Mathematics and Computer Science)

  • Tomasz Szulc

    (Adam Mickiewicz University, Faculty of Mathematics and Computer Science)

Abstract

Let A = (a ij ) and B = (b ij ) be n-by-m real matrices. Using the notion of a block P-matrix [2] we give a necessary and sufficient condition for the set r(A, B) (c(A, B), resp.) of n-by-m matrices whose rows (columns, resp.) are independent convex combinations of the rows (columns, resp.) of A and B to consist entirely of full row (column, resp.) rank matrices. This improves a result on the set r(A, B) (c(A, B), resp.) proven in [8]. Moreover, we also derive a sufficient condition for the interval of A and B, i.e., for the set i(A, B) of real n-by-m matrices (t ij a ij + (1 − t ij )b ij ) with t ij ∈ [0,1] to have the abovementioned rank property.

Suggested Citation

  • Barbara Kołodziejczak & Tomasz Szulc, 1999. "Convex Sets of Full Rank Matrices," Springer Books, in: Tibor Csendes (ed.), Developments in Reliable Computing, pages 359-364, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-1247-7_28
    DOI: 10.1007/978-94-017-1247-7_28
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