Computer generated numerical ranges and some resulting theorems

Abstract

Abstract The numerical rangeW(A), of an arbitrary n-square matrix A is the union of the numerical ranges of all 2-square real compressions of A. As a result, a simple graphics program is written that accurately exhibits W(A) for real A, and suggests several conjectures relating the geometry of W(A) to algebraic properties of A. Some of these conjectures are analyzed in the final sections of the paper. ∗The work of both authors was supported by Ihe Air Force Office of Scientific Research under grant AKOSR-83-0150. ∗The work of both authors was supported by Ihe Air Force Office of Scientific Research under grant AKOSR-83-0150. Notes ∗The work of both authors was supported by Ihe Air Force Office of Scientific Research under grant AKOSR-83-0150.