Talk:Biorthogonal system
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Incorrect example
[edit]I have a problem with the definition of cos nx, sin nx as a biorthogonal system as it is given here. It seems it is intended that we identify sin (nx)=v_n(x); cos (nx) =u_n(x); but that does not seem to satisfy the defining equation. Looks more like an orthogonal complete set to me. Maybe the example could be made more explicit or a different example that more clearly illuminates the biorthogonal property could be chosen.
Also the text in here differs from Eric Weissteins definition. Maybe someone can illuminate ?--2001:610:1908:1400:903A:F6E0:254F:8779 (talk) 16:19, 15 November 2013 (UTC)
- I agree: the example is of an orthogonal system in a single vector space, not of a biorthogonal system. I've removed it; hopefully someone can find a suitable illustrative example. A candidate example would be the dual bases in a finite-dimensional vector space and its dual basis, often used in general relativity. —Quondum 17:42, 15 November 2013 (UTC)