# Are vectors independent of reference frames?

TonyEsposito
Ok, this is the notation I am going to use in this thread: uppercase means vectors, while "[V]c" means coordinates of vector V in frame c.
I'm reading from a book: i have a reference frame "a" and a reference frame "b" rotated with respect to "a", the vector connecting the frames origin is R.
We are tracking a particle having radius vector X in frame a and X' in frame b, the book says that the relation connecting the two vector is:

X=R+Q.V'
where Q is the rotation tensor of the two frames...but arent vectors indipendent of frames? should not the relation be simply:

X=R+V'

and only when expressed in a coordinates Q comes into play?

[X]a=[R]a+Q.[V']b
[X]b=[R]b+Q^-1.[V']a

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