The Gram Matrix is also known as the Gramian matrix.
The Gram matrix of a set of vectors is the symmetric matrix of inner products.
The entries are given by G_{ij} = v_{i}^{T} v_{j} = (v_{i}  v_{j}).
v_{i}^{T} v_{j} = 

A set of vectors is linearly independent if and only if: det(G_{ij}) ≠ 0
Gram Matrix as the covariance matrix
if e_{i} represents the basis vectors then:
e^{*i} = G_{ij} e_{i}
represents the reciprocal or dual basis.
If the basis is orthogonal then G_{ij} = δ_{ij} = identity matrix and so the the basis and its dual are effectively equal.