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numerical-range:examples:2x2

Example 1

  • For a Jordan matrix $J=\begin{pmatrix}0&1\\0&0\end{pmatrix}$ the numerical range forms a circular disk of radius one half, $W(J) = D(0,\frac{1}{2})$.

Example of a circular numerical range.
Example of a circular numerical range

Example 2

  • Normal matrix of order $N=2$: the disk reduces to an interval $[\lambda_1, \lambda_2]$ in the complex plane. The matrix in the example is $M=\begin{pmatrix}1&1\ii\\-1\ii&2\end{pmatrix}$

Numerical range of a normal matrix.
Numerical range of a normal matrix

Example 3

  • Generic matrix of order $N=2$: the numerical range $W(M)$ is an ellipse. The foci of the ellipse are located in the eigenvalues. The matrix in the example is $M=\begin{pmatrix}1&1\\0&-1\end{pmatrix}$.

Numerical range of a non-normal matrix.
Numerical range of a generic matrix

numerical-range/examples/2x2.txt · Last modified: 2014/03/30 13:09 by lpawela