You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information.
| You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information.
|
Table of Contents  Math Background Matrices Linear Dependence |
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| See also: rank of a matrix |   |
| Linear (in)dependence | A given set of k vectors aj, is called linearly independent,
if the equation s1 a1
+ 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