کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5773392 1631068 2017 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
ACI-matrices of constant rank over arbitrary fields
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
ACI-matrices of constant rank over arbitrary fields
چکیده انگلیسی
The columns of an m×n ACI-matrix over a field F are independent affine subspaces of Fm. An ACI-matrix has constant rank ρ if all its completions have rank ρ. Huang and Zhan (2011) [4] characterized the m×n ACI-matrices of constant rank when |F|≥min⁡{m,n+1}. We complete their result characterizing the m×n ACI-matrices of constant rank over arbitrary fields. Quinlan and McTigue (2014) [8] proved that every partial matrix of constant rank ρ has a ρ×ρ submatrix of constant rank ρ if and only |F|≥ρ. We obtain an analogous result for ACI-matrices over arbitrary fields by introducing the concept of complete irreducibility.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 527, 15 August 2017, Pages 232-259
نویسندگان
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