Abstract
Let A be a nonnegative square matrix, and let D be a diagonal matrix whose iith element is (Ax) i x i , where x is a (fixed) positive vector. It is shown that the number of final classes of A equals n−rank( A− D). We also show that null( A− D) = null( A− D) 2, and that this subspace is spanned by a set of nonnegative elements. Our proof uses a characterization of nonnegative matrices having a positive eigenvector corresponding to their spectral radius.
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.
