| Definition: | real vector space or real point space for which a scalar product is defined for any two vectors Note 1 to entry: The usual geometrical three-dimensional space is a Euclidean point space. Four-dimensional vectors used in special relativity are elements of a non-Euclidean point space because the scalar product of a vector by itself may be negative. Another example of non-Euclidean vector space is the set of n-bit words formed of the digits zero and one with addition modulo two, because the scalar product of a vector by itself can be zero for a non-zero vector.
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