Dimension (vector Space)
In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V.
For every vector space there exists a basis (if one assumes the axiom of choice), and all bases of a vector space have equal cardinality (see dimension theorem for vector spaces); as a result the dimension of a vector space is uniquely defined. We say V is finite-dimensional if the dimension of V is finite.
The dimension of the vector space V over the field F can be written as dimF(V) or as, read "dimension of V over F". When F can be inferred from context, often just dim(V) is written.
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Famous quotes containing the word dimension:
“God cannot be seen: he is too bright for sight; nor grasped: he is too pure for touch; nor measured: for he is beyond all sense, infinite, measureless, his dimension known to himself alone.”
—Marcus Minucius Felix (2nd or 3rd cen. A.D.)