0
Let A be a matrix which is both symmetric and skew symmetric.
so AT=A and AT= -A
so A =- A
that implies 2A =zero matrix
that implies A is a zero matrix
A skew symmetric matrix is a square matrix which satisfy, Aij=-Aji or A=-At
If your graph is undirected, then its adjacency matrix will be symmetric.
Faizan
Symmetric Matrix:
Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.
note: No need to think about diagonal elements, they can be anything.
The eigen values of a real symmetric matrix are all real.