Editing Standard basis (section)

== Properties ==
By definition, the standard basis is a [[sequence]] of [[orthogonal]] [[unit vectors]]. In other words, it is an [[ordered basis|ordered]] and [[orthonormal basis|orthonormal]] basis. 

However, an ordered orthonormal basis is not necessarily a standard basis. For instance the two vectors representing a 30° rotation of the 2D standard basis described above, i.e. ,
<math display="block">v_1 = \left( {\sqrt 3 \over 2} ,  {1 \over 2} \right) \,</math>
<math display="block">v_2 = \left( {1 \over 2} , {-\sqrt 3 \over 2} \right) \,</math>
are also orthogonal unit vectors, but they are not aligned with the axes of the [[Cartesian coordinate system]], so the basis with these vectors does not meet the definition of standard basis.