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On the Numerical Ranges of Commutators

โœ Scribed by Putnam, C. R.

Book ID
120099861
Publisher
Oxford University Press
Year
1959
Tongue
English
Weight
126 KB
Volume
s1-34
Category
Article
ISSN
0024-6107

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Let A and C be n ร— n complex matrices. The C -numerical range of A is defined as the set We study classes of matrices that two matrices A, B in the respective class satisfy W C (AB) = W C (BA) for a certain complex matrix C .

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A normal form is derived for finite sets of doubly commuting matrices, under simultaneous unitary similarity. The matrices need not be normal, but they commute with each other and with the adjoints of each other. The normal form is further used to study joint numerical ranges of doubly commuting mat