Multiplicative maps on matrices that preserve the spectrum
Document Type
Article
Publication Date
1994
Abstract
Let Mn denote the set of all n×n matrices over the complex numbers (n≥ 2). Let An ⊆ Mn be either the set of all invertible matrices, the set of all unitary matrices, or a multiplicative semigroup containing the singular matrices. Theorem: If φ : An → Mn is a spectrum-preserving multiplicative map, then there exists a matrix R in Mn such that φ(S) = R−1SR for all S in An.
Publication Title
Linear Algebra and its Applications
Volume
212-213
First Page
339
Last Page
351
Digital Object Identifier (DOI)
https://doi.org/10.1016/0024-3795(94)90409-X
Citation Information
Hochwald, S. H. (1994). Multiplicative maps on matrices that preserve the spectrum. Linear Algebra and Its Applications, 212, 339–351. https://doi.org/10.1016/0024-3795(94)90409-X
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