Coates graph (original) (raw)
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 Gc(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 aji ≠ 0 then there is a directed edge from node i to node j with weight aji. In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A.
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| dbo:abstract | 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 Gc(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 aji ≠ 0 then there is a directed edge from node i to node j with weight aji. In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A. (en) En matemáticas, el gráfico de Coates o el gráfico de flujo de Coates, que lleva el nombre de C. L. Coates, es un gráfico asociado con el método de Coates para la solución de un sistema de ecuaciones lineales. El gráfico de Coates Gc (A) asociado con una matriz A n × n es un gráfico dirigido, etiquetado, ponderado y de n nodos. Los nodos, etiquetados del 1 al n, están asociados cada uno con la fila/columna correspondiente de A. Si ingresa aji ≠ 0, entonces hay un borde dirigido desde el nodo i al nodo j con un peso aji. En otras palabras, la gráfica de Coates para la matriz A es aquella cuya matriz de adyacencia es la transpuesta de A. (es) |
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| gold:hypernym | dbr:Graph |
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| rdfs:comment | 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 Gc(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 aji ≠ 0 then there is a directed edge from node i to node j with weight aji. In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A. (en) En matemáticas, el gráfico de Coates o el gráfico de flujo de Coates, que lleva el nombre de C. L. Coates, es un gráfico asociado con el método de Coates para la solución de un sistema de ecuaciones lineales. (es) |
| rdfs:label | Gráfico de Coates (es) Coates graph (en) |
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