On a Compression of Normal Matrix Polynomials

Abstract

In this article, we study a compression of normal matrices and matrix polynomials with respect to a given vector and its orthogonal complement. The numerical range of this compression satisfies special boundary properties, which are investigated in detail. The characteristic polynomial of the compression is also considered.

Keywords:

• Compression
• Eigenvalue
• Matrix polynomial
• Numerical range

Acknowledgments

The authors wish to thank J. Maroulas for several useful discussions. The authors also acknowledge with thanks an anonymous referee for his helpful suggestions and for bringing to their attention reference [5].

Notes

*E-mail: [email protected]

Additional information

Notes on contributors

Panayiotis Psarrakos

*E-mail: [email protected]