Why use a non-orthonormal basis?

Question

Geometry

Please explain what is needed and where the non-orthogonal basis is most often used.
Competence in analytical geometry in the area of ​​float( 0 ).
An additional question: why would someone need to look for the distance between two points in such a basis?

Answer 1

According to the orthographic field geometry, a non-orthogonal basis is used in the calculation of fieldmorphic quantum figures in non-basic space. If you find the distance between two points, then in theory you can measure the surface of a polymorphic figure.

Answer 2

Used in crystallography, for example.