科研之友
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摘要
Given a normal matrix A and an arbitrary square matrix B (not necessarily of the same size), what relationships between A and B, if any, guarantee that B is also a normalmatrix? We provide an answer to this question in terms of pseudospectra and norm behavior. In doing so, we prove that a certain distance formula, known to be a necessary condition for normality, is in fact sufficient and demonstrates that the spectrum of a matrix can be used to recover the spectral norm of its resolvent precisely when the matrix is normal. These results lead to new normality criteria and other interesting consequences.
- 出版日期2018
