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What is a decomposition?

What is a decomposition? Here are some definitions.

Noun
  1. A biological process through which organic material is reduced to e.g. compost
  2. The act of taking something apart, e.g. for analysis
  3. The splitting (of e.g. a matrix, an atom, or a compound) into constituent parts
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Examples
He does provide an example of the decomposition of an abelian group into cosets of a subgroup.
Come 9pm it is hard to avoid a body being dissected or a corpse in a state of decomposition.
Methane is often called marsh gas because it forms in swamps and marshes from the underwater decomposition of plant and animal material.
In the decomposition, four moles of nitroglycerin decompose into approximately 30 moles of carbon dioxide, water, nitrogen, and oxygen.
Tannin helps the leather to resist the effects of heat, decomposition by water and attack by all manner of organisms.
A variance decomposition analysis was performed to reveal the extent to which platform error influenced the ability to identify biomarkers.

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