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The Boolean rank of a nonzero m × n Boolean matrix A is the least integer k such that there are an m× k Boolean matrix B and a k × n Boolean matrix C with A = BC. We investigate the structure of linear transformations T : M m,n → M p,q which preserve Boolean rank. We also show that if a linear transformation preserves the set of Boolean rank 1 matrices and the set of Boolean rank k matrices for any k, 2 ≤ k ≤ min{m, n} (or if T strongly preserves the set of Boolean rank 1 matrices), then T preserves all Boolean ranks.
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참고문헌 (9)
참고문헌 신청
C. K. Li / 2002 / Linear transformations between matrix spaces that map one rank specific set into another / Linear Algebra Appl 357 : 197 ~ 208
G. Frobenius / 1897 / Uber die darstellung der endlichen Gruppen durch lineare Substitutioned / S. B. Deutsch. Akad. Wiss. Berlin : 994 ~ 1015
L. B. Beasley / 1984 / Boolean rank preserving operators and Boolean rank-1spaces / Linear Algebra Appl 59 : 55 ~ 77
L. B. Beasley / 1992 / Linear operators that strongly preserve upper ideals of matrices / Congr. Numer 88 : 229 ~ 244
L. B. Beasley / 2013 / Linear operators that preserve Boolean rank of Boolean matrices / Czech. Math. J 63 (2) : 435 ~ 440
G. Frobenius / 1897 / Uber die darstellung der endlichen Gruppen durch lineare Substitutioned / S. B. Deutsch. Akad. Wiss. Berlin : 994 ~ 1015
L. B. Beasley / 1984 / Boolean rank preserving operators and Boolean rank-1spaces / Linear Algebra Appl 59 : 55 ~ 77
L. B. Beasley / 1992 / Linear operators that strongly preserve upper ideals of matrices / Congr. Numer 88 : 229 ~ 244
L. B. Beasley / 2013 / Linear operators that preserve Boolean rank of Boolean matrices / Czech. Math. J 63 (2) : 435 ~ 440
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