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What is dimensional analysis?

What is dimensional analysis? Here are some definitions.

Noun
  1. (physics) The study of the dimensions of physical quantities; used to obtain information about large complex systems, and as a means of checking mathematical and physics equations.
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Examples
This relation is derived empirically through dimensional analysis.
And third, dimensional analysis, such as principal components analysis, draws conclusions from the variation in items.
On the other hand, simple dimensional analysis of the above equation yields the expectation that wing loading will increase with overall size.
They can be simplified by dimensional analysis.
Optigo outputs can be easily exported to various reverse engineering, dimensional analysis and other engineering software products such as: Geomagic, Polyworks, Metrologic, Tebis, Rapidform, etc.
Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis.

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