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Linearly Independent


Two or more functions, equations, or vectors f_1, f_2, ..., which are not linearly dependent, i.e., cannot be expressed in the form

 a_1f_1+a_2f_2+...+a_nf_n=0

with a_1, a_2, ... constants which are not all zero are said to be linearly independent.

A set of n vectors v_1, v_2, ..., v_n is linearly independent iff the matrix rank of the matrix m=(v_1 v_2 ... v_n) is n, in which case m is diagonalizable.


See also

Linearly Dependent Curves, Linearly Dependent Functions, Linearly Dependent Vectors, Matrix Rank, Maximally Linearly Independent

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Cite this as:

Weisstein, Eric W. "Linearly Independent." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LinearlyIndependent.html

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