 q) is a chart at x and v is an element of the
| vector space in which qU lies.  We say that two such triples
| (U, q, v) and (V, r, w) are &quot;equivalent&quot; if the derivative of
| rq^-1 at qx maps v on w.  The formula reads:
|
| (rq^-1)'(qx)v  =  w
|
| (obviously an equivalence relation by the chain rule).
|
| Lang, DARM, page 25.
|
| An equivalence class of such triples is called a &quot;tangent vector&quot; of X at x.
| The set of such tangent vectors is called the &quot;tangent space&quot; of X at 