Re:Viewing Matrices and Probability as Graphs
by Twisol on Wednesday March 06, 2019 @05:59PM
(#19323861)
> [...] what do matrices corresponding to equivalence relations look like?
Actually, the graphic under "Block matrices correspond to disconnected graphs" illustrates this for us already! (Just mentally replace all the non-zero entries with 1; the graphs structurally remain the same.)
I initially thought it would be "a disconnected set of cliques", but we've already established that we're modeling rectangular matrices as bipartite graphs between the input and output spaces. Square matrices in particular can be considered to operate over the same vector space, so we could have more arbitrary graphs -- such as cliques.
Actually, the graphic under "Block matrices correspond to disconnected graphs" illustrates this for us already! (Just mentally replace all the non-zero entries with 1; the graphs structurally remain the same.)
I initially thought it would be "a disconnected set of cliques", but we've already established that we're modeling rectangular matrices as bipartite graphs between the input and output spaces. Square matrices in particular can be considered to operate over the same vector space, so we could have more arbitrary graphs -- such as cliques.