Dual basis in a field extension

In mathematics, the linear algebra concept of dual basis can be applied in the context of a finite field 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 is true if L is separable over K; it is always true if K is a perfect field, including when K is finite or of characteristic zero.

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