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