Inverse eigenvalues theorem

In numerical analysis and linear algebra, the Inverse eigenvalues theorem states that, given a matrix A that is nonsingular, with eigenvalue ${\displaystyle \lambda >0}$, ${\displaystyle \lambda }$ is an eigenvalue of ${\displaystyle A}$ if and only if ${\displaystyle \lambda ^{-1}}$ is an eigenvalue of ${\displaystyle A^{-1}}$.