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... of continuity when considering functions from one matrix group to another. More importantly we can consider continuous homomorphisms, and from now on all homomorphisms will be assumed to be continuous. Then if we have two matrix groups G and H and a homomorphism φ : G → H then every curve,γ, in G wi ...
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... Then (Ak )ij is the number of paths of length k from node i to node j. In particular, (Ak )ii is the number of cycles of length k that start and end at node i, and trace(Ak ) is the total number of length k cycles starting from any node. Recalling that the trace of a matrix is the sum of the eigenva ...
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