The equation satisfied by the n × n state transition matrix Φ(t,t₀): ∂Φ(t,t₀)/∂t = A(t )= Φ(t,t₀), Φ(t₀,t₀)=I; here I is the unit n ×n matrix, and A(t ) is the n × n matrix which appears in the vector differential equation dx(t )/dt =A(t )x(t ) for the n-component state vector x(t ).