Abstract
Let V be a linear subspace of M n , p ( K ) with codimension lesser than n, where K is an arbitrary field and n ⩾ p . In a recent work of the author, it was proven that V is always spanned by its rank p matrices unless n = p = 2 and K ≃ F 2 . Here, we give a sufficient condition on codim V for V to be spanned by its rank r matrices for a given r ∈ 〚 1 , p - 1 〛 . This involves a generalization of the Gerstenhaber theorem on linear subspaces of nilpotent matrices.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
