Definition of "orthonormal" [orthonormal]

• Of a set of vectors, both orthogonal and normalized. (adjective)
• Of a linear transformation that preserves both angles and lengths. (adjective)

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• "Any collection of N mutually orthogonal vectors of length 1 in an N-dimensional vector space constitutes an orthonormal basis for that space."
• "Conversely, every orthonormal basis and every unit vector are understood to correspond to such a measurement and such a state."
• "Decoherence seems to yield a (maybe partial) solution to the problem, in that it naturally identifies a class of ˜preferred™ states (not necessarily an orthonormal basis!), and even allows to reidentify them over time, so that one can identify"