Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics Of a
set ofvectors , bothorthogonal andnormalized .  adjective mathematics Of a
linear transformation thatpreserves bothangles andlengths .
Etymologies
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Examples

Any collection of N mutually orthogonal vectors of length 1 in an Ndimensional vector space constitutes an orthonormal basis for that space.

Quantum mechanics asks us to take this literally: any ˜maximal™ discrete quantummechanical observable is modeled by an orthonormal basis, and any pure quantum mechanical state, by a unit vector in exactly this way.

A denote the collection of (unordered) orthonormal bases of H.

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

Conversely, every orthonormal basis and every unit vector are understood to correspond to such a measurement and such a state.

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”.

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.

The output state of the circuit is then measured in the computational basis, or in any other arbitrary orthonormal basis.

The special states and are known as the computational basis states, and form an orthonormal basis for this vector space.

I.e. he generated a spectrogram of the proxies using a different orthonormal basis set.
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