标题：On a conjecture about the norm of Lyapunov mappings
作者：Feng, Jun-E ;Lam, James ;Yang, Guowu ;Li, Zhao
作者机构：[Feng, Jun-E ] School of Mathematics, Shandong University, Jinan; 250100, China;[Yang, Guowu ] School of Computer Science and Engineering, University 更多
来源：Linear Algebra and Its Applications
关键词：Frobenius norm; Kronecker product; Lyapunov mapping; Non-negative matrix; Spectral norm; Spectral radius
摘要：The norm properties of Lyapunov mappings and their restrictions on symmetric and skew-symmetric subspaces are investigated. For non-negative, non-positive, and tridiagonal matrices, this paper gives an affirmative answer to an open conjecture which says that the norm of a Lyapunov mapping over the space of real square matrices equals that of its restricted map over the subspace of real symmetric matrices. In addition, matrix transformation and norm relationships on certain matrices arising from the Lyapunov mapping and its restrictions are provided. © 2014 Elsevier Inc.