Linear-independence meaning

The property of a set of vectors of having no linear combinations equal to zero unless all of the coefficients are equal to zero.
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(algebra) The state of being linearly independent.

The linear independence of a set of vectors can be determined by calculating the Gram determinant of those vectors; if their Gram determinant is zero, then they are linearly dependent, and if their Gram determinant is non-zero, then they are linearly independent. Incidentally, the same Gram determinant can be used to calculate the hyper-volume of a hyper-parallelepiped (whose edges which "radiate" from an "origin" vertex are described by the vectors).

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