کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6416285 | 1631127 | 2015 | 17 صفحه PDF | دانلود رایگان |
In this paper, we consider the problem of factorizing the nÃn matrix Jn of all ones into the nÃn binary matrices. We show that under some conditions on the factors, these are isomorphic to a row permutation of a De Bruijn matrix. Moreover, we consider in particular the binary roots of Jn, i.e. the binary solutions to Am=Jn. On the one hand, we prove that any binary root with minimum rank is isomorphic to a row permutation of a De Bruijn matrix whose row permutation is represented by a block diagonal matrix. On the other hand, we partially solve Hoffman's open problem of characterizing the binary solutions to A2=Jn by providing a characterization of the binary solutions to A2=Jn with minimum rank. Finally, we provide a class of roots which are isomorphic to a De Bruijn matrix.
Journal: Linear Algebra and its Applications - Volume 468, 1 March 2015, Pages 63-79