[permalink] [id link]
However, orthogonal matrices arise naturally from dot products, and for matrices of complex numbers that leads instead to the unitary requirement.
from
Wikipedia
Some Related Sentences
However and orthogonal
However, in a few unusual and specific domains, such as immune systems, it seems that humans prefer others who are unlike themselves ( e. g., with an orthogonal immune system ), since this will lead to a baby that has the best of both worlds.
However, spinors transform well under the infinitesimal orthogonal transformations ( like infinitesimal rotations or infinitesimal Lorentz transformations ).
However, later it was shown that such model of closed timelike curve can have internal inconsistencies as it will lead to strange phenomena like distinguishing non orthogonal quantum states and distinguishing proper and improper mixture.
where is a Sturm – Liouville operator ( However it should be noted this operator may in fact be of the form where w ( x ) is the weighting function with respect to which the eigenfunctions of are orthogonal ) in the x coordinate.
However, linear algebra includes orthogonal transformations between spaces which may be neither finite-dimensional nor of the same dimension, and these have no orthogonal matrix equivalent.
However, for bounded normal operators orthogonal complement to a stable subspace may not be stable.
However, unlike orthogonal complements, W < sup >⊥</ sup > ∩ W need not be 0.
However in most cases the functions f ( x ) can be written in terms of an infinite series of orthogonal functions such as and then the definition becomes:
However for graphical and image applications geometric fitting seeks to provide the best visual fit ; which usually means trying to minimize the orthogonal distance to the curve ( e. g., total least squares ), or to otherwise include both axes of displacement of a point from the curve.
However, if the matrix is symmetric, it is possible to use the orthogonal eigenvector to generate the second solution.
However, without a polynomial term that is orthogonal to the radial basis functions, estimates outside the fitting set tend to perform poorly.
However, because H does not correspond to an ordinary least-squares fit ( i. e. is not an orthogonal projection ), these sums-of-squares no longer have ( scaled, non-central ) chi-squared distributions, and dimensionally defined degrees-of-freedom are not useful.
However, we want our orthogonal trajectories to span every point on every circle, which means that must have a range which at least include one period of rotation.
However the correlation between experimentally determined binding affinities and the predictions of nine commonly used scoring functions have been found to be nearly orthogonal ( R < sup > 2 </ sup > ~ 0 ).
However and matrices
( However, there are other, similar matrices that are also called " Laplacian matrices " of a graph.
However, one can consider arbitrary types such as boolean values, categorical variables, complex numbers, vectors, matrices, sequences, trees, sets, shapes, manifolds, functions, and processes.
However, one needs at least 4 × 4 matrices to set up a system with the properties required — so the wave function had four components, not two, as in the Pauli theory, or one, as in the bare Schrödinger theory.
However, almost all modern computer printers also create their output as matrices of dots, but use a different technology like laser printing or inkjet printing, and are not called Dot Matrix printers.
However, matrices that can be diagonalized with the same similarity transformation do form a commutative ring.
However, they rarely appear explicitly as matrices ; their special form allows more efficient representation, such as a list of n indices.
However, there are other operations which could also be considered as a kind of addition for matrices, the direct sum and the Kronecker sum.
However, for matrices over a more general ring that need not be commutative, such as the quaternions, they may not be equal.
However, the constant coefficient hidden by the Big O notation is so large that these algorithms are only worthwhile for matrices that are too large to handle on present-day computers.
However, the eigenvalue decomposition and the singular value decomposition differ for all other matrices M: the eigenvalue decomposition is where U is not necessarily unitary and D is not necessarily positive semi-definite, while the SVD is where Σ is a diagonal positive semi-definite, and U and V are unitary matrices that are not necessarily related except through the matrix M.
However, it is not the case that all normal matrices are either unitary or ( skew -) Hermitian.
However, in the remainder of this article we will consider only square matrices.
However decoherence was largely ignored for many years, and not until the 1980s did decoherent-based explanations of the appearance of wavefunction collapse become popular, with the greater acceptance of the use of reduced density matrices.
However, the product of two Hermitian matrices A and B is Hermitian if they commute, i. e., if AB = BA.
However the complex Hermitian matrices do form a vector space over the real numbers.
However, most recent model DivX compatible DVD players have improved support for custom quantization matrices.
However, they are all of the form of a series of the simple rational functions, which have poles at the eigenvalues of the partitioned matrices.
However, if all the matrices have the same rank, will converge to.
However, electrospray ionization methods coupled with mass spectrometry allow a rapid and direct analysis of samples with complex matrices: the native liquid samples are directly ionized under ambient conditions in their original solution.
However, A ⊗ B and B ⊗ A are permutation equivalent, meaning that there exist permutation matrices P and Q such that
However, once a linear map Φ between the density matrices is specified, a standard linearity argument, together with the finite dimensional assumption, allow us to extend Φ uniquely to the full space of operators.
However and arise
However, technical difficulties arise by melting at local hot spots.
However, when labor disputes arise, its provisions come clearly into play.
However, further experience takes these equal chances, and forces the imagination to observe that certain chances arise more frequently than others.
However, complications can arise in the many-body problem.
However, this will normally only arise to negate the defence case when automatism or diminished responsibility is in issue.
However, about AD 200 small contentions arise and the people begin to be divided, ultimately leading to a " great division ".
However, the Constitutional Chamber of the Supreme Court rejected the referendum stating that " The rights of minorities that arise from anti-majoritarian claims can not be subjected to a referendum process which the majority imposes ".
However, developmental mechanisms are not understood sufficiently to explain which kinds of phenotypic variation can arise in each generation from variation at the genetic level.
However, because DCTs operate on finite, discrete sequences, two issues arise that do not apply for the continuous cosine transform.
However, this deeper model requires more insight during design, insight that may only come to light as problems arise.
However, Northern Ireland Secretary of State Peter Hain said that he was " convinced that at least one prosecution will arise out of today's report ".
However, when exceptions arise and the burden of proof has been shifted to the defendant, he is required to establish a defense that bears an " air of reality.
However, notable differences are likely to arise ; a largely contributing effect is the spin – orbit ( SO ) interaction, or, more exactly, subshell splitting.
However, resistance to trimethoprim and other drugs aimed at DHFR can arise due to a variety of mechanisms, limiting the success of their therapeutical uses.
" However, this is not creativity in the modern sense, which did not arise until the Renaissance.
However, when vacancies arise, the commissioners court of the respective county has the authority to appoint a replacement to serve out the remaining term.
However, problems began to arise from the mintage.
However, safety concerns do arise from the near-colourless flame with which alcohol burns.
However, because DSTs operate on finite, discrete sequences, two issues arise that do not apply for the continuous sine transform.
However, given the factions and jealousies that arise in any court, and that Hephaestion was supremely close to the greatest monarch the western world had yet seen, it is remarkable how little enmity he inspired.
However empty summations often arise implicitly when the range of values being added depends on certain unknown parameters, and may become empty for certain values of the parameters.
However, the disease itself is a result of a complex interplay between several factors: the worm, the symbiotic Wolbachia bacteria within the worm, the host ’ s immune response, and the numerous opportunistic infections and disorders that arise.
However, it has been pointed out that epistemological problems arise in assessing an offender's level of remorse.
However, scrapie tends to persist in flocks and can also arise apparently spontaneously in flocks that have not previously had cases of the disease.
0.786 seconds.