
In a 2D Cartesian vector space the basis is expressed in Dirac notation as An arbitrary vector is expressed in this basis as Suppose we consider a new basis rotated from the first by an angle θ as shown in the figure at the right:. 
(a) Construct the 8 dot products
.
(b) Use the dot products you have constructed to express the coordinates of the vector A> in the new basis, a_{1}', a_{2}', in terms of the old coordinates, a_{1}, a_{2}.
Last revision 28. November, 2005.