**1.6 Geometry**

In Section (1.3) we saw that if *A* ϵ *M*_{2}, then the field of values *F*(*A*) is a (possibly degenerate) ellipse with interior and that the ellipse may be determined in several ways from parameters associated with the entries of the matrix *A*.

*Exercise*. If , show that *F*(*A*) is: (a) a point if and only if *λ*_{2} = *λ*_{1} and *β* = 0; (b) a line segment joining *λ*_{1} and *λ*_{2} if and only if *β* = 0; (c) a circular disc of radius if and only if *λ*_{2} = *λ*_{1}; or (d) an ellipse (with interior) with foci at *λ*_{1} and *λ*_{2} otherwise, and *λ*_{1} and *λ*_{2} are interior points of the ...