dual basis


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dual basis

[¦dü·əl ′bā·ses]
(mathematics)
for a finite-dimensional vector space with basis x1, x2, …, xn, the dual basis of the conjugate space is the set of linear functionals f1, f2, …, fn with fi (xi) = 1 and fi (xj) = 0 for i not equal to j.
For a Barach space with basis x 1, x 2, …, the dual basis of the conjugate space is the sequence of continuous linear functionals, f1, f2, …, defined by fi (xi) = 1 and fi (xj) 0 for i not equal to j, provided that the conjugate space is shrinking.
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Key words and phrases : dual basis, spline-type space, localization.
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