Leavitt path algebras: the first decade — mentioned by blurbleblurble

Mon, 18 Dec 2017 06:35:53 GMT

Graph theory offers one nice illustration of the transpose (for square matrices). Here's a directed graph: ⬐---------¬ n₁ → n₂ → n₃ It can be represented by this adjacency matrix: X = [ 0 1 0 ] [ 0 0 1 ] [ 1 0 0 ] See how there is a 1 for each row i and column j where there is an edge from node i to node j? Okay, now look at the transpose, Xᵀ: Xᵀ = [ 0 0 1 ] [ 1 0 0 ] [ 0 1 0 ] If we interpret this matrix as an adjacency matrix, its graph looks like this: ⬐---------¬ n₃ → n₂ → n₁ Taking the transpose of a directed graph's adjacency matrix just reverses the direction of the edges! P.S: some…

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Leavitt path algebras: the first decade · HackerPapers discussions

Leavitt path algebras: the first decade — mentioned by blurbleblurble