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Let $M_n \in \mathbb{R}^{N \times N}$ be a block-tridiagonal matrix: $$M_n = \begin{bmatrix} B_1 & C_1 & 0 & 0 & \cdots & 0 \\ A_1 & B_2 & C_2 & 0 & \cdots & 0 \...

Consider the symmetric matrix $$M = \begin{bmatrix} A & B \\ B^T & -C \end{bmatrix}$$ where $A \in \cal{R}^{n \times n}$ and $C \in \cal{R}^{m\times m}$ are symmetric, ...