# Numerical Shadow

The web resource on numerical range and numerical shadow

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numerical-range:generalizations:numerical-range-of-a-with-respect-to-b

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 numerical-range:generalizations:numerical-range-of-a-with-respect-to-b [2018/10/08 09:21]plewandowska numerical-range:generalizations:numerical-range-of-a-with-respect-to-b [2018/10/08 09:21] (current)plewandowska [Definition] Both sides previous revision Previous revision 2018/10/08 09:21 plewandowska [Definition] 2018/10/08 09:21 plewandowska 2018/10/08 09:20 plewandowska [Definition] 2018/10/08 09:19 plewandowska [Definition] 2018/05/22 14:14 plewandowska 2018/05/22 14:11 plewandowska 2018/05/22 14:11 plewandowska 2018/05/22 14:10 plewandowska 2014/11/17 00:12 lpawela 2014/10/19 23:34 lpawela created 2018/10/08 09:21 plewandowska [Definition] 2018/10/08 09:21 plewandowska 2018/10/08 09:20 plewandowska [Definition] 2018/10/08 09:19 plewandowska [Definition] 2018/05/22 14:14 plewandowska 2018/05/22 14:11 plewandowska 2018/05/22 14:11 plewandowska 2018/05/22 14:10 plewandowska 2014/11/17 00:12 lpawela 2014/10/19 23:34 lpawela created Line 21: Line 21: Let $A$ be an $N \times M$ matrix, with $N > M$ given by $A=\begin{pmatrix}A_1 \\ A_2 \end{pmatrix}$ and let $\1_{N,M} = \begin{pmatrix}\1_M \\ 0\end{pmatrix}$,​ where $\1_M$ denotes an $M \times M$ identity matrix. The numerical range of $A$ is given by Let $A$ be an $N \times M$ matrix, with $N > M$ given by $A=\begin{pmatrix}A_1 \\ A_2 \end{pmatrix}$ and let $\1_{N,M} = \begin{pmatrix}\1_M \\ 0\end{pmatrix}$,​ where $\1_M$ denotes an $M \times M$ identity matrix. The numerical range of $A$ is given by $$$- W_{\|\cdot\|_2}(A;​ \mathbb{I}_{N,M}) = W(A_1), + W_{\|\cdot\|_2}(A;​ \mathbb{1}_{N,M}) = W(A_1),$$$ where $W(A_1)$ denotes the standard numerical shadow. where $W(A_1)$ denotes the standard numerical shadow.
numerical-range/generalizations/numerical-range-of-a-with-respect-to-b.txt · Last modified: 2018/10/08 09:21 by plewandowska

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