Numerical Shadow

The web resource on numerical range and numerical shadow

User Tools

Site Tools


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

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
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]
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