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On a conjecture about the norm of Lyapunov mappings. (English) Zbl 1303.15026

Summary: 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.

MSC:

15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15B48 Positive matrices and their generalizations; cones of matrices
15A18 Eigenvalues, singular values, and eigenvectors
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