کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6416021 | 1631091 | 2016 | 66 صفحه PDF | دانلود رایگان |
Let n,p,r be positive integers with nâ¥pâ¥r. A rank-râ¾ subset of n by p matrices (with entries in a field) is a subset in which every matrix has rank less than or equal to r. A classical theorem of Flanders states that the dimension of a rank-râ¾ linear subspace must be less than or equal to nr, and it characterizes the spaces with the critical dimension nr. Linear subspaces with dimension close to the critical one were later studied by Atkinson, Lloyd and Beasley over fields with large cardinality; their results were recently extended to all fields [18].Using a new method, we obtain a classification of rank-râ¾ affine subspaces with large dimension, over all fields. This classification is then used to double the range of (large) dimensions for which the structure of rank-râ¾ linear subspaces is known for all fields.
Journal: Linear Algebra and its Applications - Volume 504, 1 September 2016, Pages 124-189