On the geometry of the envelope of a matrix

نویسندگان

  • Panayiotis J. Psarrakos
  • Michael J. Tsatsomeros
چکیده

The envelope, EðAÞ, of a complex square matrix A is a region in the complex plane that contains the spectrum of A and is contained in the numerical range of A. The envelope is compact but not necessarily convex or connected. The connected components of EðAÞ have the potential of isolating the eigenvalues of A, leading us to study its geometry, boundary, and number of components. We also examine the envelope of normal matrices and similarities. In the process, we observe that EðAÞ contains the 2-rank numerical range of A. 2014 Elsevier Inc. All rights reserved.

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عنوان ژورنال:
  • Applied Mathematics and Computation

دوره 244  شماره 

صفحات  -

تاریخ انتشار 2014