Vector Space Span

The span of subspace generated by vectors and is

$Span(v_1,v_2)={rv_1+sv_2:r,s in R}.$

A set of vectors $m={v_1,...,v_n}$ can be tested to see if they span -dimensional space using the following Wolfram Language function:

  SpanningVectorsQ[m_List?MatrixQ] :=
    (NullSpace[m] == {})

See also

Linear Combination, Null Space, Vector Basis, Vector Space

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Cite this as:

Weisstein, Eric W. "Vector Space Span." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VectorSpaceSpan.html

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