假设Aa=λaAa = \lambda aAa=λa，则A−1a=1λaA^{-1}a = \frac{1}{\lambda}aA−1a=λ1a∵A−1=1∣A∣A∗A^{-1} = \frac{1}{\left|A\right|}A^*A−1=∣A∣1A∗∴A−1a=1∣A∣A∗a=1λaA^{-1}a =\frac{1}{\left|A\right|}A^*a = \frac{1}{\lambda}aA−1a=∣A∣1A∗a=λ1a∴A∗a=∣A∣λaA^*a = \frac{\left|A\right|}{\lambda}aA∗a=λ∣A∣a假设A∗a=λ∗aA^*a = \lambda^* aA∗a=λ∗a则λ∗=∣A∣λ\lambda^* = \frac{\left|A\right|}{\lambda}λ∗=λ∣A∣
