Geometrically, the Gram determinant is the square of the volume of the parallelotope formed by the vectors.
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Compare the Gram determinant of a set of vectors in an-dimensional space, which, unlike the determinant of vectors, is always positive, corresponding to a squared number.
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An important application is to compute linear independence : a set of vectors is linearly independent if and only if the Gram determinant ( the determinant of the Gram matrix ) is non-zero.
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The right-hand side is the Gram determinant of "'a "'and "'b "', the square of the area of the parallelogram defined by the vectors.
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