Numbers Menu

The Numbers menu is created dynamically when EigTool is started, using files contained in the num_comp directory, under the eigtool directory. For some items, a point may be marked on the pseudospectra plot, indicating where this numerical value is attained (see Display Points). In these cases, the point can be removed from the plot by selecting the corresponding menu item a second time (a check mark by the item indicates whether the point is displayed or not).

Eigenvector Matrix Cond. No. Compute the (2-norm) condition number of the matrix of eigenvectors.
Departure from Normality This option will compute Henrici's departure from normality for the current matrix. This is defined to be the Frobenius norm of N where N = T-diag(li), T is the Schur factor of the matrix and diag(li) is the diagonal of T.
Numerical Abscissa Compute the numerical abscissa, the rightmost point in the field of values.
Pseudospectral Abscissa Compute (for a particular value of eps) the pseudospectral abscissa, the real part of the rightmost point in the eps-pseudospectrum.
Pseudospectral Radius Compute (for a particular value of eps) the pseudospectral radius, the absolute value of the point with greatest modulus in the eps-pseudospectrum.
Spectral Abscissa Compute the spectral abscissa, the real part of the rightmost eigenvalue of the matrix.
Spectral Radius Compute the spectral radius, the absolute value of the eigenvalue with greatest modulus.
Display Points When this option is toggled on, the points in the complex plane at which the above numbers are attained, if appropriate, are marked on the pseudospectra plot. When this item is toggled off, any existing points are removed, and no more will be plotted until it is toggled again.


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