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Math Help - standard basis

  1. #1
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    standard basis

    when we say that t A is an nxn matrix whose columns are given by the vectors in S where S is a basis for R^n,

    does it mean that A is a transition matrix from S to S'' where S'' is the standard basis in R^n?

    thanks!
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  2. #2
    Member HappyJoe's Avatar
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    You are quite right.

    To elaborate, if S=\{v_1,v_2,\ldots,v_n\} is the given basis for \mathbb{R}^n, and if A is the matrix, whose ith column is the basis vector v_i, then if [a]_S is the coordinates of the vector a\in\mathbb{R}^n with respect to the (ordered) basis S, then

    A[a]_S = a,

    and the vector a can be considered as itself written in the standard basis.
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