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- W1965432015 abstract "A rank one matrix can be factored as <TEX>$mathbf{u}^tmathbf{v}$</TEX> for vectors <TEX>$mathbf{u}$</TEX> and <TEX>$mathbf{v}$</TEX> of appropriate orders. The perimeter of this rank one matrix is the number of nonzero entries in <TEX>$mathbf{u}$</TEX> plus the number of nonzero entries in <TEX>$mathbf{v}$</TEX>. A matrix of rank k is the sum of k rank one matrices. The perimeter of a matrix of rank k is the minimum of the sums of perimeters of the rank one matrices. In this article we characterize the linear operators that preserve perimeters of matrices over semirings." @default.
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- W1965432015 date "2009-01-31" @default.
- W1965432015 modified "2023-10-17" @default.
- W1965432015 title "LINEAR OPERATORS THAT PRESERVE PERIMETERS OF MATRICES OVER SEMIRINGS" @default.
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- W1965432015 doi "https://doi.org/10.4134/jkms.2009.46.1.113" @default.
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