The only possible measurement is between any two orthogonal states (an orthonormal basis). This implies that an orthonormal wavelet is self-dual. For matrices, re-normalizing the result requires converting the matrix into its nearest orthonormal representation. The eigenstates have a physical meaning further than an orthonormal basis. Every symmetric matrix is thus, up to choice of an orthonormal basis, a diagonal matrix. This is equivalent to the assertion that every Hilbert space has an orthonormal basis. Any separable inner product space has an orthonormal basis. The Gramian matrix of any orthonormal basis is the identity matrix. Consider the case of rectangular coordinate systems with orthonormal bases only. These are binary square waves that form a complete orthonormal set. In that case, "unitary" is the same as "orthonormal". Every rotation maps an orthonormal basis of formula 1 to another orthonormal basis. Written with respect to an orthonormal basis, the squared length of is . Moreover, in most Banach spaces setting there are no orthonormal bases. Let formula 32 be a local section of orthonormal bases.