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numerical-range:generalizations:restricted-numerical-range:real-numerical-range

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numerical-range:generalizations:restricted-numerical-range:real-numerical-range [2019/03/04 12:08]
plewandowska [Fact]
numerical-range:generalizations:restricted-numerical-range:real-numerical-range [2019/03/04 12:08] (current)
plewandowska [Conditions for the generalized numerical range to be real]
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 ===== Conditions for the generalized numerical range to be real ===== ===== Conditions for the generalized numerical range to be real =====
-==== Fact ==== [( :​marcus1985conditions )]+==== Fact ==== 
 The classical numerical range satisfies ​ The classical numerical range satisfies ​
 $$W(CU^\dagger AU) \subset \mathbb{R}$$ $$W(CU^\dagger AU) \subset \mathbb{R}$$
-for all unitary $U$ if and only if at least one of $C$ and $A$ is scalar and their product is hermitian.+for all unitary $U$ if and only if at least one of $C$ and $A$ is scalar and their product is hermitian ​[( :​marcus1985conditions )]
numerical-range/generalizations/restricted-numerical-range/real-numerical-range.txt · Last modified: 2019/03/04 12:08 by plewandowska