orthonormal basis in a sentence

Examples

1. A Parseval ( or tight ) unit norm frame is an orthonormal basis; such a frame satisfies Parseval's identity.
2. The commuting self-adjoint operators with odd powers of act on, so can be simultaneously diagonalized by an orthonormal basis.
3. Let "'k "'i be an orthonormal basis of states in the underlying one-particle Hilbert space.
4. In fact, in dimension n = 1, an orthonormal basis of H ^ 1 [ 0, 1 ] is given by
5. A particular case is obtained when these vectors form an orthonormal basis, that is, they are all perpendicular to each other.
6. Its rows are mutually orthogonal vectors with unit norm, so that the rows constitute an orthonormal basis of " V ".
7. Two matrices which are unitarily equivalent are also basis; unitary equivalence corresponds to a change from an orthonormal basis to another orthonormal basis.
8. Two matrices which are unitarily equivalent are also basis; unitary equivalence corresponds to a change from an orthonormal basis to another orthonormal basis.
9. :For ( 2 ), if you choose an orthonormal basis, the isometries are characterized by where they send those basis elements.
10. Every finite-dimensional inner product space has an orthonormal basis, which may be obtained from an arbitrary basis using the Gram Schmidt process.