Perturbation analysis of the canonical subspaces Original Research Article

In this note, we study the null space structure of singular real symmetric matrices with undirected graph a tree. The main result is a relationship between the dimension of the nullspace of A, the zero-nonzero pattern of the null vectors of A and the graph of A. This work extends results of Fiedler (M. Fiedler, Czechoslovak Mathematical Journal 25 (100) (1975) 607–618) [1], Wiener (G. Wiener, Linear Algebra and its Applications 61 (1984) 15–29) [2] and Parter (S. Parter, J. SIAM 8 (2) (1960) 376–388) [3].