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If we are discussing differentiable complex-valued functions, then Af and V are complex vector spaces, and Af may be any complex numbers.

We now write Af where Af are distinct complex numbers.

If Af is the null space of Af, then Theorem 12 says that Af.

In other words, if F satisfies the differential equation Af, then F is uniquely expressible in the form Af where Af satisfies the differential equation Af.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

This reduction has been accomplished by the general methods of linear algebra, i.e., by the primary decomposition theorem.