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Conversely, one-dimensional orthogonal projectors are extreme points of the set of density operators.
Some Related Sentences
Conversely and orthogonal
Conversely, given central idempotents a < sub > 1 </ sub >,..., a < sub > n </ sub > in R that are pairwise orthogonal and have sum 1, then R is the direct sum of the rings Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.
Conversely and are
Conversely, experimenters would consider as impressive such statements as the following, which, if they turned out to be hits, are so unusual as to be really significant:
Conversely, the vowel marks of the Tigrinya abugida and the Amharic abugida ( ironically, the original source of the term " abugida ") have been so completely assimilated into their consonants that the modifications are no longer systematic and have to be learned as a syllabary rather than as a segmental script.
Conversely, most heat-treatable alloys are precipitation hardening alloys, which produce the opposite effects that steel does.
Conversely, most realists ( specifically, indirect realists ) hold that perceptions or sense data are caused by mind-independent objects.
Conversely the use of true brass seems to have declined in Western Europe during this period in favour of gunmetals and other mixed alloys but by the end of the first Millennium AD brass artefacts are found in Scandinavian graves in Scotland, brass was being used in the manufacture of coins in Northumbria and there is archaeological and historical evidence for the production of brass in Germany and The Low Countries areas rich in calamine ore which would remain important centres of brass making throughout the medieval period, especially Dinant – brass objects are still collectively known as dinanterie in French.
Conversely, many fighter aircraft, such as the F-16, are often used as ' bomb trucks ,' despite being designed for aerial combat.
Conversely, the Belgian Blue's meat tenderness has been argued to be just as tender because there are a large number of smaller muscle fibers.
Conversely, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never " catch up " to very distant objects.
Conversely, certain general principles ( for example, neighbourliness, or charity ) are seen to be universal and consistent.
Conversely, modern biological sciences ( including even concepts such as molecular ecology ) are intimately entwined and dependent on the methods developed through biotechnology and what is commonly thought of as the life sciences industry.
Conversely beetles are prey of various invertebrates and vertebrates including insects, fish, reptiles, birds and mammals.
Conversely, factors that favor plate columns are: presence of solids in feed, high liquid rates, large column diameters, complex columns, columns with wide feed composition variation, columns with a chemical reaction, absorption columns, columns limited by foundation weight tolerance, low liquid rate, large turn-down ratio and those processes subject to process surges.
Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.
Conversely, there are other stars that never rise above the horizon, as seen from any given point on the Earth's surface ( except exactly on the equator ).
Conversely, Harris maintains that the fact-value distinction is a confusion, proposing that values are really a certain kind of fact.
If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.
Conversely, the tiny meson mass mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.
Conversely, BBC critic Mark Kermode believes that " the movie industries of Britain and America are inextricably intertwined ", citing numerous examples of how Hollywood provides work to British production staff and studios, whilst Britain enables Hollywood to base their prestigious productions at UK studios.
Conversely, in functional code, the output value of a function depends only on the arguments that are input to the function, so calling a function f twice with the same value for an argument x will produce the same result f ( x ) both times.
Conversely, the bodies of people who had certain medical conditions are useful for research into those conditions.
Conversely, if the data are sparse — that is, if only K out of N Fourier coefficients are nonzero — then the complexity can be reduced to O ( K log N log ( N / K )), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm ( which estimates the largest K coefficients to several decimal places ).
Conversely, rifle bullets can pierce light armor and are easier to shoot accurately, but even a carbine such as the Colt M4 is larger and / or longer than a submachine gun, making it harder to maneuver in close quarters.
Conversely, if either of these last two expressions is defined, then so is the other ( and again they are equal ).
Conversely and extreme
Conversely, surveys conducted among living donors postoperatively and in a period of five years following the procedure have shown extreme regret in a majority of the donors, who said that given the chance to repeat the procedure, they would not.
Conversely, if the difference in price is near zero, but the more costly competitor would convey an enormous battlefield advantage through special ammunition, radar fire control and laser range finding, enabling it to destroy enemy tanks accurately at extreme ranges, military planners may choose it instead — based on the same cost effectiveness principle.
Conversely, using lenses with much longer focal lengths for portraits results in more extreme flattening of facial features, which also may be objectionable to the viewer.
Conversely and points
Each convex set containing X must ( by the assumption that it is convex ) contain all convex combinations of points in X, so the set of all convex combinations is contained in the intersection of all convex sets containing X. Conversely, the set of all convex combinations is itself a convex set containing X, so it also contains the intersection of all convex sets containing X, and therefore the sets given by these two definitions must be equal.
Equipped with this notion of length, a Riemannian manifold is a metric space, meaning that it has a distance function d ( p, q ) whose value at a pair of points p and q is the distance from p to q. Conversely, the metric tensor itself is the derivative of the distance function ( taken in a suitable manner ).
Conversely, extra lives are earned by collecting heart points, which are earned by defeating enemies or collecting Hearts, with an extra life earned for every 100 points earned.
Any point x gives rise to a continuous function p < sub > x </ sub > from the one element topological space 1 ( all subsets of which are open ) to the space X by defining p < sub > x </ sub >( 1 ) = x. Conversely, any function from 1 to X clearly determines one point: the element that it " points " to.
Conversely, points are deducted from a panellist who gives " answers which are not only wrong, but pathetically obvious ", typically answers that are generally believed to be true but in fact are not.
Conversely, if the length-scale decreases and the physical parameters approach fixed values, then we have ultraviolet fixed points.
Conversely, Mark Chapman's England's Amateurs site states that the 1908 and 1912 teams were Great Britain, and points to the fact that photographic evidence shows the team playing with the Union flag on their shirts.
Conversely, a pixel in a zoomed region of a Buddhabrot image can be affected by initial points from regions far outside the one being rendered.
Conversely, iteration may give the appearance of points diverging away from a single point ; this would be the case for an unstable fixed point.
Conversely, the perennial strategy may sometimes be the more effective survival strategy, because the plant has a head start every spring with growing points, roots, and stored energy that have survived through the winter.
Conversely, any pair of lattice points with this property constitute a fundamental pair, and furthermore, they generate the same lattice.
Conversely, Clover points out that the villain of slasher films is often a male whose masculinity, and sexuality more generally, are in crisis.
This rational curve sends the zeros of G to each of the coordinate points of ; that is, all but one of the vanish for a zero of G. Conversely, any rational normal curve passing through the n + 1 coordinate points may be written parametrically in this way.
Conversely, the histogram for a very bright image with few dark areas and / or shadows will have most of its data points on the right side and center of the graph.