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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- October 19th 2010, 02:07 AMalexandrabel90standard 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! - October 19th 2010, 07:12 AMHappyJoe
You are quite right.

To elaborate, if is the given basis for , and if is the matrix, whose th column is the basis vector , then if is the coordinates of the vector with respect to the (ordered) basis , then

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