In mathematics, in graph theory, the **Seidel adjacency matrix** of a simple undirected graph *G* is a symmetric matrix with a row and column for each vertex, having 0 on the diagonal, −1 for positions whose rows and columns correspond to adjacent vertices, and +1 for positions corresponding to non-adjacent vertices.
It is also called the **Seidel matrix** or—its original name—the (−1,1,0)-**adjacency matrix**.
It can be interpreted as the result of subtracting the adjacency matrix of *G* from the adjacency matrix of the complement of *G*.

The multiset of eigenvalues of this matrix is called the **Seidel spectrum**.

The Seidel matrix was introduced by J. H. van Lint and Johan Jacob Seidel in 1966 and extensively exploited by Seidel and coauthors.

The Seidel matrix of *G* is also the adjacency matrix of a signed complete graph *K _{G}* in which the edges of

The eigenvalue properties of the Seidel matrix are valuable in the study of strongly regular graphs.