On the numerical range of some block matrices with scalar diagonal blocks

ABSTRACT

Several new verifiable conditions are established for matrices of the form $\left[\begin{array}{cc}\alpha I_{n-k}& C\\ D& \text{β}{I}_k\end{array}\right]$ to have the numerical range equal the convex hull of at most k ellipses. For k = 2, these conditions are also necessary, provided that the ellipses are co-centred.

Keywords:

• Numerical range

Acknowledgments

The results are partially based on the Capstone project of the first named author [TG] under the supervision of the second named author [IMS]. This work was supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi.