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Span

  • Definition: If S = {v_1, v_2, … , v_k} is a set of vectors in R^n , then the set of all linear combinations of v_1, v_2, … , v_k is called the span of v_1, v_2, … , v_k and is denoted by span(v_1, v_2, … , v_k) or span(S). If span(S) = R^n, then S is called a spanning set. (We can define the span of a set of matrices to be the set of all linear combinations of the matrices.)

    Source: Linear Algebra: A Modern Introduction, 3rd edition by David Poole (note-custom edition titled Matrix Algebra)

  • Listed under: Linear Algebra, Abstract Algebra

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