Show that $v_1,...,v_n$ form an orthonormal basis of $\mathbb{R^n}$ for the inner product $\langle v,w\rangle = v^TKw$ for $K > 0$ iff $A^TKA = I$ where $A= (v_1v_2...v_n)$.
How will I be able to do this problem? I know that in order to be an orthonormal basis it must have a unit vector equal to one and must be orthogonal, but how will I be able to show that here?