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=== Conceptual modeling ===
Formally, an array ''A'' is given by a (total or partial) function ''A'': ''X'' → ''V'' where ''X'', the ''___domain'' is a ''d''-dimensional integer interval for some {{math|''d'' > 0}} and ''V'', called ''range'', is some (non-empty) value set; in set notation, this can be rewritten as {{math|{{mset| (''p'',''v'') | ''p'' ∈ ''X'', ''v'' ∈ ''V'' }}}}. Each (''p'',''v'') in ''A'' denotes an array element or ''cell'', and following common notation we write ''A''[''p''] = ''v''. Examples for ''X'' include {0..767} × {0..1023} (for [[Xga#Extended Graphics Array|XGA]] sized images), examples for ''V'' include {0..255} for 8-bit [[greyscale
Following established database practice, an array query language should be [[Declarative programming|declarative]] and safe in evaluation.
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The following are representative domains in which large-scale multi-dimensional array data are handled:
*Earth sciences: geodesy / mapping, [[remote sensing]], geology, oceanography, hydrology, atmospheric sciences, cryospheric sciences
*Space sciences: Planetary sciences, astrophysics (optical and radio telescope observations, cosmological simulations)
*Life sciences: gene data, confocal microscopy, CAT scans
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