numerical range of self-inverse matrices

for an n×n matrix a, let m(a) be the smallest possible constant in the inquality d_p(a) ≤ m(a)rp(a). here p is a point on the smooth portion of the boundary ∂w(a) of the numerical range a. r_p(a) is the radius of curvature of ∂w(a) at this point, and d_p(a) is the distance from p to the spectrum ofa. in this paper we compute them(a) for matrix a is self-invers. 200 mathematics subject classification. primary 47a12; secondary 15a42, 14h50.