[行列解析1.2.P13]

A = \begin{pmatrix}
B & y^* \\
x & a
\end{pmatrix} \in M_{n+1}

p_A(t) = (t - a) p_B(t) - y^* \operatorname{adj}(t I - B) x
\tag{1.2.19}

p_A(t) = (t - \lambda)^{n-1} \left[ t^2 - (a + \lambda) t + a\lambda - y^* x \right]
\tag{1.2.20}

\begin{pmatrix}
\lambda I_n & y^* \\
x & a
\end{pmatrix}

\frac{a + \lambda \pm \sqrt{(a - \lambda)^2 + 4 y^* x}}{2}