write the coordinates of v .
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v = x1v1 + x2v2 + ··· + xnvn, where xi ∈ R. The coefficients x1,x2,...,xn are called the coordinates of v with respect to the ordered basis v1,v2,...,vn. is a one-to-one correspondence between V and Rn. This correspondence respects linear operations in V and in Rn.
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