On Sat, Nov 11, 2017 at 1:12 PM, Jed Brown <[email protected]> wrote:
> Matthew Knepley <[email protected]> writes: > > >> Matrix and graph are equivalent concepts. > > > > > > This is clearly wrong. A matrix is the coordinate representation of a > > linear operator, and thus has a specific > > behavior under coordinate transformations. A graph is just connectivity, > > and really just a relation. I cannot > > count the number of times Barry has ranted about this on petsc-maint > > (usually about Vecs and arrays). The > > mathematical object is not its data structure. > > A graph Laplacian certainly does transform under coordinate > transformation and indeed, we use that property to design effective > coarsening strategies. That one basis strikes you as intrinsically > "more canonical" does not mean it isn't a linear operator. > That is one operator. This is argument by anecdote. An arbitrary graph is not a linear operator, but an arbitrary matrix definitely is (the coordinate representation of one). Matt -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
