and construct a rate-constant matrix whose entries are the . Also, let be the vector of concentrations as a function of time. Let be the vector of ones. Let be the identity matrix. Let be the function that takes a vector and constructs a diagonal matrix whose on-diagonal entries are those of the vector. Let be the inverse Laplace transform from to . Then the time-evolved state is given by thus providing the relation between the initial conditions of the system and its state at time . See also Michaelis–Menten kinetics Molecularity Petersen matrix Reaction–diffusion system Reactions on surfaces: rate equations for reactions where at least one of the reactants adsorbs onto a surface Reaction progress kinetic analysis Reaction rate Reaction rate constant Steady state approximation Gillespie algorithm Balance equation Belousov-Zhabotinsky reaction Lotka–Volterra equations Chemical kinetics References Books cited External links Chemical kinetics, reaction rate, and order (needs flash player) Reaction kinetics, examples of important rate laws (lecture with audio). Rates of Reaction Chemical kinetics Chemical reaction engineering cy:Cyfradd adwaith#Hafaliadau cyfradd