Lets say we have two basis. Let B={b} and C={_{1},b_{2}c} Then the change of coordinate matrix P(C to B) involves the C-coordinate vectors of_{1},c_{2}band_{1}bLet_{2}.

[b]_{1}_{c}=[x_{1}] and [b]_{2}=[y1]_{c}

////////[x_{2}]//////////////[y2].

Then by definition [c_{1}c][x1]=_{2}band [_{1}c_{1}c][y1]=_{2}bI dont get how you can multiply the matrix with basis set C with the change of coordinate matrix P(C to B) to get back basis set B ?_{2. }

/////////////////////////////[x2]/////////////////// [y2]

Can anyone elaborate on that thanks.