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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2008.1
- 수록면
- 465 - 472 (8page)
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초록· 키워드
오류제보하기
For a nonnegative real matrix A of rank 1, A can be factored as ab^t for some
vectors a and b. The perimeter of A is the number of nonzero entries in both a and b. If B
is a matrix of rank k, then B is the sum of k matrices of rank 1. The perimeter of B is the
minimum of the sums of perimeters of k matrices of rank 1, where the minimum is taken
over all possible rank-1 decompositions of B. In this paper, we obtain characterizations of
the linear operators which preserve perimeters 2 and k for some k≥4. That is, a linear
operator T preserves perimeters 2 and k(≥4) if and only if it has the form T(A) = UAV , or T(A) = UA^tV with some invertible matrices U and V .
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참고문헌 (8)
참고문헌 신청
A. Berman / 1976 / Nonegative matrices in the mathematical sciences / Academic, New York
C. K. Li / 2001 / Linear preserver problems / Amer. Math. Monthly 108 : 591 ~ 605
L. B. Beasley / / Column ranks and their preservers over nonnegative real matrices / Linear Algebra Appl., to appear
L. B. Beasley / 1984 / Pullman, Boolean rank-preserving operators and Boolean rank-1 spaces / Linear Algebra Appl 59 : 55 ~ 77
L. B. Beasley / 1985 / Nonnegative rank-preserving operators / Linear Algebra Appl 65 : 207 ~ 223
C. K. Li / 2001 / Linear preserver problems / Amer. Math. Monthly 108 : 591 ~ 605
L. B. Beasley / / Column ranks and their preservers over nonnegative real matrices / Linear Algebra Appl., to appear
L. B. Beasley / 1984 / Pullman, Boolean rank-preserving operators and Boolean rank-1 spaces / Linear Algebra Appl 59 : 55 ~ 77
L. B. Beasley / 1985 / Nonnegative rank-preserving operators / Linear Algebra Appl 65 : 207 ~ 223
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