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.
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© 1999 Springer Science+Business Media Dordrecht
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Kołodziejczak, B., Szulc, T. (1999). Convex Sets of Full Rank Matrices. In: Csendes, T. (eds) Developments in Reliable Computing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1247-7_28
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DOI: https://doi.org/10.1007/978-94-017-1247-7_28
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5350-3
Online ISBN: 978-94-017-1247-7
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