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Principal eigenvector of non-negative symmetric block matrix is approximated by a linear combination of the principal eigenvectors of the blocks

Let $ M \in \mathbb{R}^{n \times n} = \begin{bmatrix} A & B \\ B^T & C \end{bmatrix} $ for some nonnegative $A \in \mathbb{R}^{k \times k}, B \in \mathbb{R}^{k \times n-k}, C \in \mathbb{R}^{n-...
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Simple random walk on a discrete torus - the eigensystem, reference

My problem concerns finding a reference in which the formulae for the eigenvalues and the corresponding eigenvectors ($n$ linearly independent eigenvectors!) for the transition matrix of a simple ...
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