I have questions about the inner product and coordinate transformation matrix. For F inner product space V, consider vector a and b in V and its inner product <a,b> then the inner product is invariant about changing the Basis of V?
And let B and B' be Basiss of V. Then can I think that the coordinate transformation matrix from B to B', denoted by R is a unitary matrix because it preserves the inner product <a,b>?