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Near Extensions and Alignment of Data in R(superscript)n
book

Near Extensions and Alignment of Data in R(superscript)n

by Steven B. Damelin
November 2023
Intermediate to advanced content levelIntermediate to advanced
192 pages
3h 29m
English
Wiley
Content preview from Near Extensions and Alignment of Data in R(superscript)n

3 Counterexample to Theorem 2.2 (part (1)) for card (E)> d See [39]

We observe immediately the restriction k less-than-or-equal-to d (recall k equals normal c normal a normal r normal d left-parenthesis upper E right-parenthesis for the existence of the extension normal upper Phi in Theorem 2.2 (part (1)). Is this simply a “technical issue”? The answer to this “optimistic” guess is no.

The k less-than-or-equal-to d sufficient condition for the existence of the extension normal upper Phi turns out to be deeper than merely “sufficient” as a tool. In fact, under the geometry of upper E given by Theorem 2.2, the extension normal upper Phi does not always exist for k > d. In this chapter we will provide the required counterexample. In fact, the  >  case under the geometry of the finite ...

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ISBN: 9781394196777Purchase Link