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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]
Last updated: 10-24-2005 01:20:01
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details