A definition of numerical range of rectangular matrices
Ch. Chorianopoulos, Sotirios Karanasios, Panayiotis Psarrakos · Linear and Multilinear Algebra · 2009
Bonsall and Duncan (1973) observed that the numerical range of a bounded linear operator can be written as an infinite intersection of closed circular discs. Motivated by this interesting property (which does not seem to be very popular with people working on numerical ranges), we propose a definition of numerical range of rectangular complex matrices. The new range is always compact and convex, and satisfies basic properties of the standard numerical range. Our analysis is based on the properties of norms and the Birkhoff–James orthogonality.