Abstract
In the case of a finite-dimensional linear space L, the dual, or conjugate, space L* consisting of all linear functionals on L plays an important role in the general theory. The primary result in the finite-dimensional case is that the natural injection of L into the dual L** of L is an isomorphism of L onto L**. This means that if x is an element of L and x** denotes the element of L** given by the equation x**(f) = f(x) for all f in L*, then the map x → x** is one-to-one from L onto L**.
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© 1978 Springer-Verlag Berlin Heidelberg
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Segal, I.E., Kunze, R.A. (1978). Function Spaces. In: Integrals and Operators. Grundlehren der mathematischen Wissenschaften, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66693-3_6
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DOI: https://doi.org/10.1007/978-3-642-66693-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66695-7
Online ISBN: 978-3-642-66693-3
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