ON THE FIELD OF VALUES OF A MATRIX

W is clearly a compact and connected set. Toeplitz showed in [3] that W has a convex outer boundary, and a short time later F. Hausdorff [1] proved that W itself is convex. Since then several investigations have been made concerning the geometry of W. An example of a recent one is the dissertation of R. Kippenhahn [2] in which W is described as the convex hull of a certain algebraic curve of degree n obtainable from C. Writing