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What is a dimensionality?

What is a dimensionality? Here are some definitions.

Noun
  1. The state or characteristic of possessing dimensions.
  2. (mathematics) The number of dimensions something has.
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Examples
In order to determine the dimensionality of the scales, factor analysis with varimax rotation was undertaken.
Such rephrasing suggests a generalization of the concept of a vector to spaces of dimensionality higher than three.
With so many majestic shots and brilliant cinematography, I wanted more depth and dimensionality from the transfer.
In physics one might look for infinities in space, time, divisibility, or dimensionality.
Other potential applications for dimensionality reduction techniques, primarily in natural language analysis, will also be addressed.
He feels that the true theory may be independent of any dimensionality of space-time, and that 11 dimensions only emerges once one tries to solve it.

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