A set of vectors is maximally linearly independent if including any other vector in the vector space would make it linearly dependent (i.e., if any other vector in the space can be expressed as a linear combination of elements of a maximal set--the basis).

# Maximally Linearly Independent

## See also

Basis, Linearly Dependent Vectors, Vector, Vector Space## Explore with Wolfram|Alpha

## Cite this as:

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