Dimension (metadata)
Encyclopedia
In metadata
, dimension is a set of equivalent units of measure, where equivalence between two units of measure is determined by the existence of a quantity preserving one-to-one correspondence between values measured in one unit of measure and values measured in the other unit of measure, independent of context, and where characterizing operations are the same.
The equivalence defined here forms an equivalence relation on the set
of all units of measure. Each equivalence class corresponds to a
dimensionality. The units of measure "temperature in degrees Fahrenheit"
and "temperature in degrees Celsius" have the same dimensionality, because
given a value measured in degrees Fahrenheit there is a value measured in
degrees Celsius with the same quantity, and vice-versa. Quantity preserving
one-to-one correspondences are the well-known equations Cº = (5/9)*(Fº − 32)
and Fº = (9/5)*(Cº) + 32.
Units of measure are not limited to physical categories.
Examples of physical categories are: linear measure, area, volume, mass,
velocity, time duration.
Examples of non-physical categories are: currency, quality indicator, colour
intensity
Quantities may be grouped together into categories of quantities which
are mutually comparable. Lengths, diameters, distances, heights, wavelengths
and so on would constitute such a category. Mutually comparable quantities
have the same dimensionality. ISO 31-0
calls these quantities of the same
kind.
Metadata
The term metadata is an ambiguous term which is used for two fundamentally different concepts . Although the expression "data about data" is often used, it does not apply to both in the same way. Structural metadata, the design and specification of data structures, cannot be about data, because at...
, dimension is a set of equivalent units of measure, where equivalence between two units of measure is determined by the existence of a quantity preserving one-to-one correspondence between values measured in one unit of measure and values measured in the other unit of measure, independent of context, and where characterizing operations are the same.
The equivalence defined here forms an equivalence relation on the set
of all units of measure. Each equivalence class corresponds to a
dimensionality. The units of measure "temperature in degrees Fahrenheit"
and "temperature in degrees Celsius" have the same dimensionality, because
given a value measured in degrees Fahrenheit there is a value measured in
degrees Celsius with the same quantity, and vice-versa. Quantity preserving
one-to-one correspondences are the well-known equations Cº = (5/9)*(Fº − 32)
and Fº = (9/5)*(Cº) + 32.
Units of measure are not limited to physical categories.
Examples of physical categories are: linear measure, area, volume, mass,
velocity, time duration.
Examples of non-physical categories are: currency, quality indicator, colour
intensity
Quantities may be grouped together into categories of quantities which
are mutually comparable. Lengths, diameters, distances, heights, wavelengths
and so on would constitute such a category. Mutually comparable quantities
have the same dimensionality. ISO 31-0
ISO 31-0
ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the SI...
calls these quantities of the same
kind.