linear span

The span of subspace generated by vectors v_1 and v_2 element V is Span(v_1, v_2) congruent {r v_1 + s v_2 :r, s element R}. A set of vectors m = {v_1, ..., v_n} can be tested to see if they span n-dimensional space using the following Wolfram Language function: SpanningVectorsQ[m_List?MatrixQ] := (NullSpace[m] == {})

linear combination | null space | vector basis | vector space