Examples
For example, the standard basis vectors of R2 (the Cartesian plane) are
and the standard basis vectors of its dual space R2* are
In 3-dimensional Euclidean space, for a given basis {e1, e2, e3}, you can find the biorthogonal (dual) basis by these formulas:
where T denotes the transpose and
is the volume of the parallelepiped formed by the basis vectors and
Read more about this topic: Dual Basis
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