Numerical Shadow

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numerical-shadow:generalizations:restricted-numerical-shadow:real-numerical-shadow

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numerical-shadow:generalizations:restricted-numerical-shadow:real-numerical-shadow [2013/04/16 00:54]
lpawela generalizations:real-numerical-shadow renamed to numerical-shadow:generalizations:restricted-numerical-shadow:real-numerical-shadow
numerical-shadow:generalizations:restricted-numerical-shadow:real-numerical-shadow [2013/08/03 21:00]
lpawela
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 ===== Definition ===== ===== Definition =====
  
-Real numerical shadow of a matrix $A$ is defined as a probability ditribution $P_A(z)$ on the complex plane, supported on the [[generalizations:​real-numerical-range|real numerical range]] $W^\mathbb{R}(A)$.+Real numerical shadow of a matrix $A$ is defined as a probability ditribution $P_A(z)$ on the complex plane, supported on the [[numerical-range:​generalizations:​restricted-numerical-range:​real-numerical-range|real numerical range]] $W^\mathbb{R}(A)$.
 $$ $$
 P_A(z) := \int_{\Omega} {\rm d} \mu(\psi) \delta\Bigl( z-\langle \psi|A|\psi\rangle\Bigr),​ P_A(z) := \int_{\Omega} {\rm d} \mu(\psi) \delta\Bigl( z-\langle \psi|A|\psi\rangle\Bigr),​
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 ===== Examples ===== ===== Examples =====
-  * [[specialcases:​2x2#​hermitian_matrices|Real shadow of 2x2 Hermitian matrices]] +  * [[numerical-shadow:​examples:​2x2#​hermitian_matrices|Real shadow of 2x2 Hermitian matrices]] 
-  * [[specialcases:​3x3#​hermitian_matrices|Real shadow of 3x3 Hermitian matrices]] +  * [[numerical-shadow:​examples:​3x3#​hermitian_matrices|Real shadow of 3x3 Hermitian matrices]] 
-  * [[specialcases:​4x4#​hermitian_matrices|Real shadow of 4x4 Hermitian matrices]] +  * [[numerical-shadow:​examples:​4x4#​hermitian_matrices|Real shadow of 4x4 Hermitian matrices]] 
-  * [[specialcases:​4x4#​non-normal_matrices|Real shadow of 4x4 non-normal matrices]]+  * [[numerical-shadow:​examples:​4x4#​non-normal_matrices|Real shadow of 4x4 non-normal matrices]]
numerical-shadow/generalizations/restricted-numerical-shadow/real-numerical-shadow.txt · Last modified: 2018/10/08 08:55 by plewandowska