| 释义 |
linearly dependent and independent A set of vectors u1, u2,…, ur is linearly independent if x1u1 + x2u2 + … + xrur = 0 implies x1 = 0, x2 = 0,…, xr = 0. Otherwise, the set is linearly dependent. A set of two vectors is linearly independent if and only if the two are not parallel or, in other words, if and only if neither is a scalar multiple of the other. In 3‐dimensional space, any set of four or more vectors must be linearly dependent, and a set of three vectors is linearly independent if and only if the three are not coplanar. See basis.
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