I can't believe there's any one answer, partially because it's a way of looking at 'things' - culture, organisation, science, aspects of the physical world, so it supposes the artificial in most cases. For example, an organisation isn't of itself a matrix but can be made to appear like one on the basis of the way it's made to work - reporting lines.
For many it's simpler to think of things this way rather than as 'systems'.
The only technical definition is mathematical and possibly crystals and rocks.
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