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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 a_{j}, is called linearly independent, if the equation s_{1}a_{1} + s_{2}a_{2} + ... + s_{k}a_{k} = o has no other solution than the trivial one (all scalars s_{j} are zero). If any scalars s_{j} 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