拉普拉斯矩阵群逆的分块表示

Block Representation of Laplacian Matrix Group Inverse

令G为具有拉普拉斯矩阵L(G)和无符号拉普拉斯矩阵Q(G)的加权图。根据L(G)的广义舒尔补的群可逆条件,以及拉普拉斯矩阵的其它性质,利用分块矩阵求群逆的计算方法,计算L(G)群逆的分块表达式。并通过例子说明计算结果。

Let G be a weighted graph with Laplacian matrix L(G) and signless Laplacian matrix Q(G). According to the group invertibility condition of the generalized Schur complement of L(G) and other properties of Laplacian matrix. An expression for the group inverse of L(G) is calculated by using the method of group inverse of block matrix. Moreover, an example has been constructed to illustrate the result.