Can a Matrix A Equalize Vectors u and v in Different Reference Frames?

taybasta
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Hi everyone,

Given two different reference frames in a vector space; say left and right. v is a vector defined in the left frame and u is a vector defined in the right frame.
What is the nature of a matrix A that can satisfy the equality u= A.v?
Thank you
 
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If the vector space has dimension n, then A is represented by the n by n, non-singular, matrix whose columns are the coefficients of vectors in u when written as a linear combination of the vectors in v.
 
Thanks HallsofIvy,
the problem is that the two vectors u and v are not defined in the same reference frame.
 

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