Definitions
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- adjective mathematics Of a
set ofvectors , bothorthogonal andnormalized . - adjective mathematics Of a
linear transformation thatpreserves bothangles andlengths .
Etymologies
from Wiktionary, Creative Commons Attribution/Share-Alike License
Examples
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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.
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Quantum mechanics asks us to take this literally: any ˜maximal™ discrete quantum-mechanical observable is modeled by an orthonormal basis, and any pure quantum mechanical state, by a unit vector in exactly this way.
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A denote the collection of (unordered) orthonormal bases of H.
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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
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Conversely, every orthonormal basis and every unit vector are understood to correspond to such a measurement and such a state.
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When we perform a series of transformations into orthonormal frames at a series of points along the path, and the redshift is still exactly the same, and we go “ooooh look, now we have a series of Doppler shifts along the path”.
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Usually this measurement is done in the computational basis, but since quantum mechanics allows one to express an arbitrary state as a linear combination of basis states, provided that the states are orthonormal (a condition that ensures normalization) one can in principle measure the register in any arbitrary orthonormal basis.
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The output state of the circuit is then measured in the computational basis, or in any other arbitrary orthonormal basis.
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The special states and are known as the computational basis states, and form an orthonormal basis for this vector space.
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I.e. he generated a spectrogram of the proxies using a different orthonormal basis set.
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