Invariant manifold

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Min-plus matrix multiplication, also known as the distance product, is an operation on matrices.

Given two n×n matrices A=(aij) and B=(bij), their distance product C=(cij)=AB is defined as an n×n matrix such that cij=mink=1n{aik+bkj}.

This operation is closely related to the shortest path problem. If W is an n×n matrix containing the edge weights of a graph, then Wk gives the distances between vertices using paths of length at most k edges, and Wn is the distance matrix of the graph.

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See also

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