# Rigidity matrix

The d-dimensional rigidity matrix of a framework (G,p) is a matrix $R(G,p) \in \mathbb{R}^{|E| \times d|V|}$ defined as follows. Each row represents an edge while the columns are grouped into sets of d columns, each group representing a node. For an edge $uv \in E$, the d entries corresponding to a node u (respectively the node v) are the d different coordinates of the vector p(u)-p(v) (respectively p(v)-p(u)). The rest of the entries are zeroes.