Editing Stream function (section)

=== In terms of vector rotation ===
The velocity <math>\mathbf{u}</math> can be expressed in terms of the stream function <math>\psi</math> as
:<math>
\mathbf{u} = - R \, \nabla \psi
</math>
where <math>R</math> is the <math>3 \times 3</math> rotation matrix corresponding to a <math>90^\circ</math> anticlockwise rotation about the positive <math>z</math> axis. Solving the above equation for <math>\nabla \psi</math> produces the equivalent form
:<math>
\nabla \psi = R\, \mathbf{u}.
</math>
From these forms it is immediately evident that the vectors <math>\mathbf{u}</math> and <math>\nabla \psi</math> are
* perpendicular:  <math> \mathbf{u} \cdot \nabla \psi = 0 </math>
* of the same length:  <math> |\mathbf{u}| = |\nabla \psi| </math>.
Additionally, the compactness of the rotation form facilitates manipulations (e.g., see [[Stream function#Condition of existence|Condition of existence]]).