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While the state transition matrix φ is not completely unknown, it must always satisfy the following relationships:
:<math>\frac{\partial \phi(t, t_0)}{\partial t} = A(t)\phi(t, t_0)</math> and
:<math>\phi(\tau, \tau) = I</math> for all <math>\tau</math> and where <math>I</math> is the [[identity matrix]].
And φ also must have the following properties:
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