7

It seems to me that what the vector contains is a probability vector of resetting a random walk onto the corresponding vertex? Yes, an un-normalized probability vector. Introduction to PageRank The PageRank score is based on the idea of a web surfer randomly clicking through links, i.e. a random walk on the directed graph of webpages and links. After each ...


5

James F. Feagin's Quantum Methods with Mathematica book has an elegant implementation of this in chapter 15.1 Commutator Algebra. It's along the lines of @Sjoerd's answer (but figured I'd provide the reference to the book above), first defining typical identities for the NonCommutativeMultiply symbol: Unprotect[NonCommutativeMultiply]; A_ ** (B_ + C_) := A *...


5

I think I've figured it out, but I haven't checked it super carefully so buyer beware: Unprotect[NonCommutativeMultiply]; ClearAll[NonCommutativeMultiply]; NonCommutativeMultiply[] := 1; NonCommutativeMultiply[a_] := a; NonCommutativeMultiply[first___, const_?NumericQ*b_, rest___] := const*NonCommutativeMultiply[first, b, rest]; NonCommutativeMultiply[...


4

The link for Tensorial above is dead, you may find something interesting on J. F. Gouyet's page. I prefer in general not to use packages and make my own simple cooking. Also there are two functions Subscript and Index with almost same formats but slightly different syntaxes and definitions. Index was introduced in V10. Using Subscript may be more careful ...


2

That can be done with the NCAlgebra (non-commutative algebra) package, see the documentation. Example: (* Import package *) << NC` << NCAlgebra` << NCGBX` SetNonCommutative[x, y, px, py] SetMonomialOrder[x, y, px, py] (* x to the left, p to the right *) NCSetOutput[NonCommutativeMultiply -> True] (* pretty output *) (* commutation ...


2

I attempted installation of the MathLie package on Windows 10 by placing it in the AddOns/Packages folder… You've placed the files in wrong place. As mentioned in SetupMathLie.nb, the MathLie folder should be copied to FileNameJoin[{$TopDirectory, "AddOns", "Applications"}] // SystemOpen Then just execute $MathLiePath = FileNameJoin[{$...


1

edges = {a -> c, b -> c}; TransitiveReductionGraph[Graph[#, edges], VertexLabels -> Placed[{"Name", "Index"}, {Before, After}], GraphLayout -> {"LayeredEmbedding", "Orientation" -> Top}, PlotLabel -> Row[{"VertexList: ", #}]] & /@ Permutations[{a, b, c}] // ...


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