orthonormal

• “Any collection of N mutually orthogonal vectors of length 1 in an N-dimensional vector space constitutes an orthonormal basis for that space.”

  Quantum Mechanics

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

  Fictionaut: Puppet X: 1

• “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”

  Fictionaut: ...anything but love...

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

  Fictionaut: Puppet X: 1

• “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.”

  Fictionaut: Puppet X: 1

• “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”.”

  Does Space Expand?

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

  Quantum Computing

• “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.”

  Quantum Computing

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

  Quantum Computing

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

  The RE Benchmark in A&W « Climate Audit

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