Editing Unit vector (section)

==Curvilinear coordinates==
In general, a coordinate system may be uniquely specified using a number of [[Linear independence|linearly independent]] unit vectors <math alt="e-hat sub n">\mathbf{\hat{e}}_n</math><ref name=":0" /> (the actual number being equal to the degrees of freedom of the space). For ordinary 3-space, these vectors may be denoted <math alt="e-hat sub 1, e-hat sub 2, e-hat sub 3">\mathbf{\hat{e}}_1, \mathbf{\hat{e}}_2, \mathbf{\hat{e}}_3</math>. It is nearly always convenient to define the system to be orthonormal and [[Right-hand rule|right-handed]]:

:<math alt="e-hat sub i dot e-hat sub j equals Kronecker delta of i and j">\mathbf{\hat{e}}_i \cdot \mathbf{\hat{e}}_j = \delta_{ij} </math>
:<math alt="e-hat sub i dot e-hat sub j cross e-hat sub k = epsilon sub ijk">\mathbf{\hat{e}}_i \cdot (\mathbf{\hat{e}}_j \times \mathbf{\hat{e}}_k) = \varepsilon_{ijk} </math>

where <math> \delta_{ij} </math> is the [[Kronecker delta]] (which is 1 for ''i'' = ''j'', and 0 otherwise) and  <math alt="epsilon sub i,j,k"> \varepsilon_{ijk} </math> is the [[Levi-Civita symbol]] (which is 1 for permutations ordered as ''ijk'', and −1 for permutations ordered as ''kji'').