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 alsoBasis, Linearly Dependent Vectors, Vector, Vector Space
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Cite this as:
Weisstein, Eric W. "Maximally Linearly Independent." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MaximallyLinearlyIndependent.html