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Gram matrix
The Gram matrix of a matrix $\gc{\M}$ is the matrix
\[\gc{\M}^T\gc{\M} \p\]This is very common matrix. It is, for example, used to express the coavarance of a distribution, or the sample covariance of a dataset.
The Gram matrix is guaranteed to be positive semi-definite. If the columns of $\gc{\M}$ are linearly independent, then the Gram matrix is positive definite, and therefore invertible. If the columns are not linealy independent, the Gram matrix is singular.