Gram matrix
= Gram matrix
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{wiki}
For vectors $v_1,\ldots,v_n$, the Gram matrix is
$$
G_{ij}=\langle v_i,v_j\rangle.
$$
Two finite vector families with the same Gram matrix are related by an isometry between their spans; in finite dimensions that isometry can be extended to a unitary map after completing orthonormal bases.