FACTOID # 21: 15% of Army recruits from South Dakota are Native American, which is roughly the same percentage for female Army recruits in the state.

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Encyclopedia > Biorthogonal system

In mathematics, a biorthogonal system in a pair of topological vector spaces E and F that are in duality is a pair of indexed subsets

vi in E

and

wi in F

such that

<vi,wj> = δij

with the Kronecker delta. This applies, for example, with E = F = H a Hilbert space; in which case this reduces to an orthonormal system. In L2[0,2π] the functions cos nx and sin nx form a biorthogonal system.

## Reference

• Jean Dieudonné, On biorthogonal systems Michigan Math. J. 2 (1953), no. 1, 7–20 [1] (http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.mmj/1028989861)

Results from FactBites:

 Riesz basicity of the system of exponents with degenerated coefficients. (309 words) Riesz basicity of the system of exponents with degenerated coefficients. It is quite obvious that this sequence is biorthogonal coefficient of the functions Â are biorthogonal coefficients of this function on system (1).
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