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$v$ is a vector of length $n$, where $v_1 = 1$ and every element $v_i \in [0,1]$ $w = \| v \|_1^1 = \sum_i |v_i| = \sum_i v_i$ $x = \| v \|_2^2 = \sum_i |v_i|^2 = \sum_i v_i^2$ $y = \| v \|_3^3 = \...

I'm working on a problem that involves vectors and scalar values, and I'm looking for a closed-form solution. I hope someone can help me with this or provide insights into how to approach it. Here's ...

Statement Let $G = (V, E)$ be a connected, unweighted, and undirected graph with $n$ nodes, represented by its adjacency matrix $A$. Suppose each node $i$ is associated with a unit vector $ \mathbf{v}...