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I'm trying to find the eigenvector corresponding to the second smallest eigenvalue of a large $(4,000,000 \times 4,000,000)$ matrix $L$. $L$ is a graph Laplacian, with the following structure: $L = D -...

Consider a matrix $A\in\mathbb{R}^{n\times n}$ and a projector $P\in\mathbb{R}^{n\times n}$. Are there results regarding the generalized eigenpairs $(v,\lambda)$ of the generalized eigenproblem $$...

Consider the following problem that is known to be non-convex but can be solved as a generalized eigenvalue problem (i.e. has a global optimum solution): $\underset{w}{\text{maximize}}\quad w^{\top}...