On certain type of preconditioning for KKT-matrices (Q1878767)

The author explains why the matrix \(\mathcal M=\mathcal G^{-1}\mathcal A\), where \[ \mathcal G=\begin{pmatrix} G & B^{T} \\ B & 0 \end{pmatrix} ,\,\mathcal A=\begin{pmatrix} A & B^{T} \\ B & 0 \end{pmatrix} . \] (\(A\) is a square \(n\times n\)-matrix and \(B\) is an \(m\times n\)-matrix) has the eigenvalue 1 of multiplicity at least \(2m\).