Of fundamental importance in describing a neuron's activity and constructing biologically plausible neural networks is the unambiguous description of its smallest element of input in the integration process. Among neuronal input units are the synaptic spines: highly regulated and coordinated elements on the dendrites, exchanging both electrical signals and molecules with the soma along the dendritic branches. Mapping the physiological parameters of dendritic branches and their spines in anatomically compatible coordinates is important because of the interactions between "close" spines and between spines and the soma. We present a simple method for quantitatively locating dendritic spines by separating their coordinates into two components. The first takes into account the position of the dendritic branch on which the spine lies. In this component, the distance between a branch and the soma is given by the number of bifurcations along the dendrite ("level"). We have formulaically described the difference in this parameter between any two spines ("distance") in terms of the level of the common bifurcation farthest from the soma ("generator"). The second component of a spine's location is its position on the dendritic branch. Our system is fully analytical and easily implementable. It also defines a biologically plausible distance between any two spines, and between a spine and the soma. Based on this labeling method, we present a coordinate system in which a spine is described by a matrix encoding physiological parameters of the generating branches. A second set of coordinates is introduced to describe a neural state with a matrix of spine parameters. Finally, a third matrix notation is proposed to take into account interactions between spines. This treatment leads to some interesting speculations, such as the possibility of describing input dynamics of a neuron in terms of operators on vector spaces.