Coates graph

In mathematics, the Coates graph or Coates flow graph, named after C.L. Coates, is a graph associated with the Coates' method for the solution of a system of linear equations.

The Coates graph G_c(A) associated with an n × n matrix A is an n-node, weighted, labeled, directed graph. The nodes, labeled 1 through n, are each associated with the corresponding row/column of A. If entry a_ji ≠ 0 then there is a directed edge from node i to node j with weight a_ji. In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A.

单词	Coates graph
释义	Coates graph 英语百科 Coates graph In mathematics, the Coates graph or Coates flow graph, named after C.L. Coates, is a graph associated with the Coates' method for the solution of a system of linear equations. The Coates graph G_c(A) associated with an n × n matrix A is an n-node, weighted, labeled, directed graph. The nodes, labeled 1 through n, are each associated with the corresponding row/column of A. If entry a_ji ≠ 0 then there is a directed edge from node i to node j with weight a_ji. In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A.
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