Spielman says in Lecture 3: Laplacians and Adjacency Matrices
Fiedler’s Theorem will follow from an analysis of the eigenvalues of tri-diagonal matrices with zero row-sums. These may be viewed as Laplacians of weighted path graphs in which some edges are allowed to have negative weights. Proposition 3.1.3. Let M be a symmetric matrix such that $M \mathbf{1}=\mathbf{0}$
Then, $M =\sum_{i\neq j}−M (i, j)L(i,j).$
Proof. The expression on the right-hand side of (3.1) clearly agrees with M in all off-diagonal entries. Given all the off-diagonal entries, the diagonal entries are determined by the constraint M 1 = 0, which the right-hand side of (3.1) satisfies as well because L(i,j)1 = 0 for all i = j.
My question is What does M equals a summatory sign means? I think L is the Laplacian Matrix of M, but i'm not sure either.