Coordinate (linear algebra, $x_j=b_j^{\ast }(x)$)

A coordinate of a vector in a chosen basis is one entry of its coordinate vector. The corresponding coordinate functional in the dual basis extracts it. For an orthonormal basis, it can instead be read as an inner product with the basis vector, as in orthonormal eigenbasis. For a nonorthogonal basis, ordinary dot products need not give the coordinates.