Gramian matrix

Gramian matrix, Gram matrix or Gramian of a set of vectors V₁,..,V_n; in an inner product space is the Hermitian matrix(a square matrix with complex entries that is equal to its own conjugate transpose) of inner products, whose entries are given by  G_ij= [V_j, V_i]. For finite-dimensional real vectors with the usual Euclidean dot product, the Gram matrix is simply  G=V^TV; where V is a matrix whose columns are the vectors V_k

An important application is to compute linear independence: a set of vectors is linearly independent if and only if the Gram determinant (the determinant of the Gram matrix) is non-zero.