Editing Geographic coordinate conversion (section)

====Orthogonality====
The [[Orthogonal coordinates|orthogonality]] of the coordinates is confirmed via differentiation:
:<math>\begin{align}
  \begin{pmatrix} dX \\ dY \\ dZ \end{pmatrix} &= 
    \begin{pmatrix}
      -\sin\lambda & -\sin\phi \cos\lambda & \cos\phi \cos\lambda \\
       \cos\lambda & -\sin\phi \sin\lambda & \cos\phi \sin\lambda \\
                  0 & \cos\phi             & \sin\phi             \\
    \end{pmatrix} 
    \begin{pmatrix} dE \\ dN \\ dU \end{pmatrix}, \\[3pt]
  \begin{pmatrix} dE \\ dN \\ dU \end{pmatrix} &=
    \begin{pmatrix}
      \left(N(\phi) + h\right) \cos\phi &           0 & 0 \\
                                      0 & M(\phi) + h & 0 \\
                                      0 &           0 & 1 \\
    \end{pmatrix}
    \begin{pmatrix} d\lambda \\ d\phi \\ dh \end{pmatrix},
\end{align}</math>
<!--
: <math>\begin{align}
      & \big(dX,\, dY,\, dZ\big) \\[6pt]
    = & \big(-\sin\phi \cos\lambda,\, -\sin\phi \sin\lambda,\, \cos\phi\big) \left(M(\phi) + h\right)\, d\phi \\[6pt]
      &{}+ \big(-\sin\lambda,\, \cos\lambda,\, 0\big)\left(N(\phi) + h\right) \cos\phi\, d\lambda \\[6pt]
      &{}+ \big(\cos\lambda \cos\phi,\, \cos\phi \sin\lambda,\, \sin\phi\big)\, dh,
\end{align}</math>
-->

where
:<math>
 M(\phi) = \frac{a\left(1 - e^2\right)}{\left(1 - e^2 \sin^2 \phi\right)^\frac{3}{2}} = N(\phi) \frac{1 - e^2}{1 - e^2\sin^2\phi}
</math>

(see also "[[Meridian arc#Definition|Meridian arc on the ellipsoid]]").
<!--
The infinitesimal length caused by latitude and longitude is calculated as follows (see also "[[Meridian arc#Meridian distance on the ellipsoid|Meridian arc on the ellipsoid]]"):
: <math>
 ds^2 = \left(\frac{a\left(1 - e^2\right)}{\left(1 - e^2 \sin^2\phi\right)^\frac{3}{2}} + h\right)^2 d\phi^2 + \left(\frac{a}{\sqrt{1 - e^2 \sin^2\phi}} + h\right)^2 \cos^2\phi\, d\lambda^2 .
</math>
-->