کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4600082 | 1336834 | 2013 | 11 صفحه PDF | دانلود رایگان |
We first prove two new spectral properties for symmetric nonnegative tensors. We prove a maximum property for the largest H-eigenvalue of a symmetric nonnegative tensor, and establish some bounds for this eigenvalue via row sums of that tensor. We show that if an eigenvalue of a symmetric nonnegative tensor has a positive H-eigenvector, then this eigenvalue is the largest H-eigenvalue of that tensor. We also give a necessary and sufficient condition for this. We then introduce copositive tensors. This concept extends the concept of copositive matrices. Symmetric nonnegative tensors and positive semi-definite tensors are examples of copositive tensors. The diagonal elements of a copositive tensor must be nonnegative. We show that if each sum of a diagonal element and all the negative off-diagonal elements in the same row of a real symmetric tensor is nonnegative, then that tensor is a copositive tensor. Some further properties of copositive tensors are discussed.
Journal: Linear Algebra and its Applications - Volume 439, Issue 1, 1 July 2013, Pages 228-238