Almost every vector space we have encountered has been infinite in size (an exception is Example VSS). But some are bigger and richer than others. Dimension, once suitably defined, will be a measure of the size of a vector space, and a useful tool for studying its properties. You probably already have a rough notion of what a mathematical definition of dimension might be — try to forget these imprecise ideas and go with the new ones given here.

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##### Equivalence theorem: the matrix A has rank n. math.la.t.equiv.rank

##### Equivalence theorem: the nullity of the matrix A is zero. math.la.t.equiv.nullity