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|Table of Contents Math Background Matrices Linear Dependence|
|See also: rank of a matrix|
|Linear (in)dependence||A given set of k vectors aj, is called linearly independent, if the equation s1a1 + s2a2 + ... + skak = o has no other solution than the trivial one (all scalars sj are zero). If any scalars sj different from zero exist, the set of vectors is called linearly dependent.|
Linear independence is important for many aspects of data analysis. A general rule is that a set of n vectors of order m shows linear dependence if n is greater than m.
Linear independence is closely related to the rank of a matrix. If we
recognize a matrix as a set of n (row or column) vectors, we immediately
see that linear dependence among row or column vectors reduces the rank
of the matrix.
Last Update: 2005-Jul-16