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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] (current) 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: 2019/03/01 16:45 by plewandowska
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