Examples
Most commonly, the vectors are elements of an Euclidean space, or are functions in an L2 space, such as continuous functions on a compact interval (which are a subspace of L 2).
Given real-valued functions on the interval, the Gram matrix, is given by the standard inner product on functions:
Given a real matrix A, the matrix ATA is a Gram matrix (of the columns of A), while the matrix AAT is the Gram matrix of the rows of A.
For a general bilinear form B on a finite-dimensional vector space over any field we can define a Gram matrix G attached to a set of vectors by . The matrix will be symmetric if the bilinear form B is symmetric.
Read more about this topic: Gramian Matrix
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