determinant of linear maps

Let V be the vector space of functions which are linear combinations of
1, cos x, sin x, cos 2x, sin 2x, . . . , cos(N x), sin(N x).

Let φ : V → V be the linear map

φ(f ) =∫ f (u) du. between x and 0


Calculate det φ.


I am not sure what basis to use for V when solving this. Any help would be appreciated

Quote:

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Originally Posted by beano2913

Let V be the vector space of functions which are linear combinations of 1, cos x, sin x, cos 2x, sin 2x, . . . , cos(N x), sin(N x). Let φ : V → V be the linear map φ(f ) =∫ f (u) du. between x and 0 Calculate det φ.

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is not well defined. Consider for example then, and .