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- W2011241618 abstract "A pair of m × n matrices ( A , B ) is said to be rank-sum-maximal if ρ ( A + B )= ρ ( A )+ ρ ( B ), and rank-sum-minimal if ρ ( A + B )=| ρ ( A )− ρ ( B )|. We characterize the linear operators preserving the set of rank-sum-maximal pairs over any field and the linear operators preserving the set of rank-sum-minimal pairs over any field except for {0,1}. The linear preservers of the set of rank-sum-maximal pairs are characterized by using a result about rank preservers proposed by Li and Pierce [Amer. Math. Monthly 108 (2001) 591–605], and thereby the linear preservers of the set of rank-sum-minimal pairs are characterized. The paper can be viewed as a supplementary version of several related results." @default.
- W2011241618 created "2016-06-24" @default.
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- W2011241618 date "2003-12-01" @default.
- W2011241618 modified "2023-09-28" @default.
- W2011241618 title "Linear operators that preserve pairs of matrices which satisfy extreme rank properties––a supplementary version" @default.
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- W2011241618 doi "https://doi.org/10.1016/s0024-3795(03)00658-x" @default.
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