orthonormal basis

In other words, it is an ordered and orthonormal basis.

The result does not depend on the choice of orthonormal basis.

Any complete inner product space V has an orthonormal basis.

Let and complete this to get an orthonormal basis at .

The eigenstates have a physical meaning further than an orthonormal basis.

The set of wavefunctions is an orthonormal basis for the band in question.

More generally, the same identity holds with the e replaced by any orthonormal basis.

The only possible measurement is between any two orthogonal states (an orthonormal basis).

The density operator is defined with respect to a complete orthonormal basis.

(a) S can be extended to an orthonormal basis for V.

Indeed, each point just reflects the contribution of a given orthonormal basis function to the sum.

However, an ordered orthonormal basis is not necessarily a standard basis.

In other words, every eigenspace has an orthonormal basis of eigenvectors.

A uniform normalized tight frame with is an orthonormal basis.

The theorem that every Hilbert space has an orthonormal basis.

Each set of eigenspinors forms a complete, orthonormal basis.

The two previous theorems raise the question of whether all inner product spaces have an orthonormal basis.

Bandelets are an orthonormal basis that is adapted to geometric boundaries.

In particular, Banach spaces lack a notion analogous to an orthonormal basis.

To convert them to an orthonormal basis, we can use the Gram-Schmidt process.

Thus an orthonormal basis can be chosen on each eigenspace so that:

They are all special cases of decompositions over an orthonormal basis of an inner product space.

The corresponding normalised eigenfunctions form an orthonormal basis of H.

The sines and cosines in the Fourier series are an example of an orthonormal basis.

Now, let's choose an orthonormal basis for the fibers of T. The rest is index manipulation.