In linear algebra, the Gram matrix (or Gramian matrix, Gramian) of a set of vectors v1,…,vn{\displaystyle v_{1},\dots ,v_{n}} in an inner product space is the Hermitian matrix of inner products, whose entries are given by the inner product Gij=⟨vi,vj⟩{\displaystyle G_{ij}=\left\langle v_{i},v_{j}\right\rangle }. If the vectors v1,…,vn{\displaystyle v_{1},\dots ,v_{n}} are the columns of matrix X{\displaystyle X} then the Gram matrix is X†X{\displaystyle X^{\dagger }X} in the general case that the vector coordinates are complex numbers, which simplifies to X⊤X{\displaystyle X^{\top }X} for the case...