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.

This is an orthonormal system but it is not complete.

Let and complete this to get an orthonormal basis at .

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

"We've measured and drawn the first orthonormal base," Charles said.

Here the frames are required to be orthonormal with respect to the metric.

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

The normalisation is chosen such that if the functions are orthonormal.

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

In symbols, a basis is orthonormal if if and for each i.

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

A collection of orthonormal eigenvectors are called the principal directions.

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.

Let be a local section of orthonormal bases.

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

We can easily choose to use another orthonormal coordinate system () instead.

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.

If the basis vectors are orthonormal, then this is the unit pseudoscalar.

Each set of eigenspinors forms a complete, orthonormal basis.