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1) The name vector is applied to objects that exhibit certain
invariances with respect to certain transformations.
-- The magnitude of a vector is invariant under rotation.
-- Ditto for reflection.
-- The direction of one vector relative to another is
invariant under rotation.
-- Ditto for reflection.
2) The name pseudovector is applied to objects that exhibit
certain invariances with respect to certain transformations.
Pseudovectors behave the same under rotation but change sign
under reflection.
Vectors (and pseudovectors) in D=3 space can be represented
by an array of three numbers. The converse is not true; not
every array of three numbers is a vector. It could just be
a shopping list, with no particular transformation properties.