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numerical-range:generalizations:c-numerical-range

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numerical-range:generalizations:c-numerical-range [2019/03/01 16:44]
plewandowska [Properties]
numerical-range:generalizations:c-numerical-range [2019/03/01 16:45]
plewandowska [Properties]
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   - $\overline{W_C(A)} = W_C(\overline{A}) \iff \overline{C} \in \mathcal{U}(C)$   - $\overline{W_C(A)} = W_C(\overline{A}) \iff \overline{C} \in \mathcal{U}(C)$
   - $\overline{W_C(A)} = W_C(A^\dagger) \iff C^\dagger \in \mathcal{U}(C)$   - $\overline{W_C(A)} = W_C(A^\dagger) \iff C^\dagger \in \mathcal{U}(C)$
-  - If $c=[1,​0,​\ldots,​0]$,​ then $W_c(A)$ reduces to the classical numerical range of $A$ and if $C=\mathmr{\;​diag}(1,​0,​\ldots,​0)$,​ then $W_C(A)$ reduces to the classical numerical range of $A$.+  - If $c=[1,​0,​\ldots,​0]$,​ then $W_c(A)$ reduces to the classical numerical range of $A$ and if $C=\mathrm{\;​diag}(1,​0,​\ldots,​0)$,​ then $W_C(A)$ reduces to the classical numerical range of $A$.
  
 ===== Convexity ===== ===== Convexity =====
numerical-range/generalizations/c-numerical-range.txt · Last modified: 2020/05/16 10:42 by plewandowska