Linear Algebra 2.8 Definitions

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Linear Algebra 2.8 Definitions
2013-03-10 23:58:44
Linear Algebra Definitions

Linear Algebra Definitions
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  1. Subspace
    Closed under addition and scalar multiplication.

    • Rn is a subspace of itself.
    • Zero subspace is a subspace of Rn--set consisting of only the zero vector in Rn.

    • The zero vector is in H
    • For each u and v in H, the sum u + v is in H
    • For each u in H and each scalar c, the vector cu is in H.
  2. Column Space
    the set of Col A of all linear combinations of the columns of A

    pivot columns of A (not row reduced) form basis for column space of A.
  3. Null Space
    set of Nul A of all solutions of the homogeneous equation Ax = 0

    • Nul A is a subspace of Rn.
    • The set of solutions of a system of Ax = 0 is also a subspace of Rn.
  4. Basis
    a linearly independent set in H that spans H

    Row reduce Ax=0, put into vector equation form, and the vectors are the basis
  5. Row Space
    rows with pivots in row reduced matrix