S.E.W. Assistant Prof.
Dept. of Mathematics
Univ .of California, San Diego
APM 5763
9500 Gilman Drive
Dept. of Mathematics
UC San Diego
La Jolla, CA 92093-0112
Phone : 1(858)534-2126
Fax : 1(858)534-5273
E-mail :
(e-mail is the best way to reach me)
|  FIGURE: Smoke matrix, pseudospecta and multiple eigenvalues The  -pseudospectrum of the smoke matrix (the eigenvalues of all matrices within an neighborhood) when plotted for various resembles smoke. For smallthe-pseudospectrum
(of any matrix of size n with distinct eigenvalues) consists of n disjoint
bounded components in the complex plane. As it turns out the
smallest such
that two components coalesce is the distance to the nearest matrix with
a multiple eigenvalue. In the figure the green curve corresponds to the boundary
of the-pseudospectrum for smallest so that the components of the pseudospectrum coalesce.
The red and blue asterisks are the points of coalesences that happen
to correspond to eigenvalues whose multiplicities become two and three
under smallest perturbations possible. The black dots are the eigenvalues of the smoke matrix. See the related talk See the related paper (click on the pseudospectra to see a picture of myself) |