Definition of "real-valued" [real-valued]

• Having only real values: having as its codomain the set of real numbers or a subset thereof. (adjective)

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• "There are many examples in the literature defining a vector (vector field) as a triple of real numbers (real-valued functions) which transform in a certain way under certain coordinate changes."
• "As I said above, gij is not the metric tensor, or a tensor at all, but a set of real-valued function specified for a local coordinate system (gij are also the matrix elements in the matrix representation – in those coordinates – of the metric tensor)."
• "The sketchiness of an individual is measured, like the skewness of any given real-valued variable, by the combination of several dimensions of behavior -- communication based on technicality, obfuscation, ambiguity, tonality, diversion, digression, and ratio of chocolate chips to dough."