. .. , Dans ce cas, la matrice A peutêtreécrite sous la forme d'une matrice diagonale par bloc, après une permutation de lignes et de colonnes

, La permutation des lignes de la matrice A peutêtre formalisée comme la multiplicatio? a gauche de la matrice A par la matrice de permutation P , qui est la matrice d'identité ayant des lignes réordonnées. Alors, le polyèdre A.x un ? b est décrit comme suit : P.A

, la matrice A par la matrice de permutation Q, qui est la matrice d'identité ayant des colonnes réordonnées. En outre, la permutation des colonnes de A conduità une permutation des variables de x un (permutation des lignes de x un ). Par conséquent, cette permutation conduità la multiplicationà gauche de x un par la matrice de permutation Q . Comme Q = Q ?1 (une propriété des matrices de permutation)

. Avec-a-d-=-p.a.q,-x-d-=-q,

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