Dual basis in a field extension

In mathematics, the linear algebra concept of dual basis can be applied in the context of a finite extension L/K, by using the field trace. This requires the property that the field trace TrL/K provides a non-degenerate quadratic form over K. This can be guaranteed if the extension is separable; it is automatically true if K is a perfect field, and hence in the cases where K is finite, or of characteristic zero.

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