Conversely, every orthonormal basis and every unit vector are understood to correspond to such a measurement and such a state. ❋ Unknown (2009)
A denote the collection of (unordered) orthonormal bases of H. ❋ Unknown (2009)
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 ❋ Unknown (2009)
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. ❋ Unknown (2009)
Any collection of N mutually orthogonal vectors of length 1 in an N-dimensional vector space constitutes an orthonormal basis for that space. ❋ Ismael, Jenann (2009)
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”. ❋ Sean (2008)
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. ❋ Hagar, Amit (2007)
The output state of the circuit is then measured in the computational basis, or in any other arbitrary orthonormal basis. ❋ Hagar, Amit (2007)
The special states and are known as the computational basis states, and form an orthonormal basis for this vector space. ❋ Hagar, Amit (2007)
Now if the inverse exists and keeping in mind U columns are orthonormal, than with modest effort one can show that UT*à…⪠= à…⫔*à…⪠= Identity_matrix and à…⪭U = 0_matrix, so one can say that U=à…⪠or one can get exact reconstruction RPCs during the calibration period. ❋ Unknown (2006)
In Zorita et al JC may 2003 which has been referenced by Mann as supporting his reconstruction, they proceed directly to annual PCs by doing a svd on the standardize yearly T matrix resulting in orthonormal PCs. ❋ Unknown (2006)
Steve, normally the PCs in a PCA type analysis are columns of a unitary matrix, so the PCs columns of the unitary matrix are orthonormal to each. ❋ Unknown (2006)
Another point: because the temperature target series are averages of monthly PC series, they are very close to being orthogonal (though not orthonormal) so the temperature covariance matrix is close to being diagonal (as Jean S has independently observed.) ❋ Unknown (2006)
I.e. he generated a spectrogram of the proxies using a different orthonormal basis set. ❋ Unknown (2006)
Now in MBH, the monthly PCs are orthonormal and the U series entering into the calculations are annual averages and are no longer orthonormal. ❋ Unknown (2006)
It's called Orthonormal Basis, which the adorably apple-cheeked blogger defines thusly: ...an orthonormal basis is a set of vectors that gives you a simple way to describe your location in a vector space. ❋ Mirtika (2006)
Wahl and Ammann calculate temperature PCs annually maintaining orthogonality at this stage, but then truncate like Mann, so, once again, they are not orthonormal or orthogonal, thought they are close to it. ❋ Unknown (2006)
The resulting series are no longer orthonormal; they are close to being orthogonal but depart from orthogonality. ❋ Unknown (2006)
Normally the PC are orthonormal and it would be possible to exactly reconstruct the retained PC during the calibration period given conditions necessary for the inverse to exist. ❋ Unknown (2006)
"[My friends] in [Chicago] are [definitely] orthonormal." ❋ He Who Shall Remain Nameless (2008)
Hey [Jim] - I caught [your sister] [rug munching] one of her friends.
You've got an orthonormal gay-sis! ❋ Leonard_999 (2009)
