This paper presents a necessary and sufficient condition for diagonal stability when the digraph describing the structure of the matrix conforms to a “cactus” structure, which means that a pair of ...

The Matrix-Tree Theorem is a formula for the number of spanning trees of a graph in terms of the determinant of a certain matrix. Kirchhoff's theorem relies on the notion of the Laplacian matrix of a ...

1. R is reflexive if and only if every diagonal entry of A is 1. 2. R is symmetric if and only if A is a symmetric matrix. With a suitable ... to shift the focus of algebraic graph theory from ...

where the nonzero diagonal entries of the upper triangular matrix R in the QR decomposition of HS are all equal to each other. The precoder and the resulting successive-cancellation detector have the ...