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Gramian Matrix




:G= {Link without Title} ,\,\,G_{ij}=\int_{t_0}^{t_f} l_i( au)l_j( au)\, d au
The functions are linearly independent if and only if G is Nonsingular . Its Determinant is known as the Gram determinant or '''Gramian'''.

In fact this is a special case of a quantitative measure of linear independence of vectors, available in any Hilbert Space .

All eigenvalues of a Gramian matrix are real and non-negative and the matrix is thus also Positive Semidefinite .