The columns of the Jacobian matrix 
, 
and 
,
are the tangent vectors to the grid lines with varying 
and 
,
respectively. These vectors and define a local
coordinate system at each point and are known as covariant base
vectors 
(3.3-7) (see Figure 3.3-5).
The rows of the inverse Jacobian 
(3.3-8),
and 
, are the normal vectors to a coordinate surface
on which the coordinate respectively is constant. Also these vectors
define a local coordinate system at each point and are known as contravariant base vectors 
(3.3-9)
(see Figure 3.3-5).
