Linear operators that preserve perimeters of matrices over semirings
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A rank one matrix can be factored as u(^t)v for vectors u and v of appropriate orders. The perimeter of this rank one matrix is the number of nonzero entries in u plus the number of nonzero entries in v. 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.
Abstract
A rank one matrix can be factored as u(^t)v for vectors u and v of appropriate orders. The perimeter of this rank one matrix is the number of nonzero entries in u plus the number of nonzero entries in v. 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.
참고문헌 (6)
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