文摘
Let A be an a2851fab3b92ce8a891d" title="Click to view the MathML source">n×n complex matrix. A ternary form associated to A is defined as the homogeneous polynomial a6466f39fa7d999b" title="Click to view the MathML source">FA(t,x,y)=det(tIn+xℜ(A)+yℑ(A)). We prove, for a unitary boarding matrix A , the ternary form e52be653a58acd7f3b9c264e3f9cb2fb" title="Click to view the MathML source">FA(t,x,y) is strongly hyperbolic and the algebraic curve e6b9f42ff67a670ccdb" title="Click to view the MathML source">FA(t,x,y)=0 has no real singular points. As a consequence, we obtain that the higher rank numerical range of a unitary boarding matrix is strictly convex.