Numerical Shadow

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numerical-range

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numerical-range [2018/10/08 07:48]
plewandowska [Definition]
numerical-range [2018/10/08 07:49] (current)
plewandowska
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 ===== Definition ===== ===== Definition =====
  
-For any square matrix $A$ of size $d$, one defines its //numerical range// (also called //field of values// [( :​murnaghan1932field )]) as a subset of the complex plane: ​+For any square matrix $A$ of dimension ​$d$, one defines its //numerical range// (also called //field of values// [( :​murnaghan1932field )]) as a subset of the complex plane: ​
 $$ $$
 W(A)=\{ z \in \mathbb{C}: z=\bra{\psi} A\ket{\psi},​ \ \ket{\psi} \in {\mathbb{C}}^d,​ \ \braket{\psi}{\psi}=1\}. ​ W(A)=\{ z \in \mathbb{C}: z=\bra{\psi} A\ket{\psi},​ \ \ket{\psi} \in {\mathbb{C}}^d,​ \ \braket{\psi}{\psi}=1\}. ​
numerical-range.txt · Last modified: 2018/10/08 07:49 by plewandowska