I am reading a paper on spectral graph theory. Let us say we have an adjacency matrix W and a degree matrix D. We construct a Laplacian matrix, L defined as:
L = D - W
The paper claims that L is positive semi-definite and that the smallest eigenvalue of L is 0.
I can prove that L is positive semi-definite. But I am having trouble with understanding how the lowest eigenvalue is 0. Is this a general property of positive semi-definite matrices?