Page "Symmetric algebra" ¶ 16
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## Some Related Sentences

Conversely and symmetric
Conversely, if R is a symmetric relation over a set X, one can interpret it as describing an undirected graph with the elements of X as the vertices and the pairs in R as the edges.
Conversely, given a quadratic form in n variables, its coefficients can be arranged into an n × n symmetric matrix.
Thus, b < sub > q </ sub > is a symmetric bilinear form over K with matrix A. Conversely, any symmetric bilinear form b defines a quadratic form
Conversely, parahydrogen with an antisymmetric nuclear spin function, can only have rotational wavefunctions that are symmetric with respect to permutation of the two protons.
To summarize, M is a symmetric space G / K with a compact isotropy group K. Conversely, symmetric spaces with compact isotropy group are Riemannian symmetric spaces, although not necessarily in a unique way.
Conversely, given a pair of symmetric 2-forms h and k, the Kulkarni – Nomizu product of h and k

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 defined
Conversely, when one wants to compute an arbitrary number ( N ) of discrete samples of one cycle of a continuous DTFT, it can be done by computing the relatively simple DFT of s < sub > N </ sub >, as defined above.
Given a vector space V over a field K, the span of a set S ( not necessarily finite ) is defined to be the intersection W of all subspaces of V which contain S. W is referred to as the subspace spanned by S, or by the vectors in S. Conversely, S is called a spanning set of W.
Conversely, in a field, the expression is always defined if b is not equal to zero.
Conversely, given any partially defined operator U which is isometric on its domain ( which is not
Conversely, using the last line as a definition one shows that the expression so defined is a connection compatible with the metric, i. e. is a Levi-Civita connection.
Conversely, a function u: E < sub > 1 </ sub > → E < sub > 2 </ sub > defined on a basis of E < sub > 1 </ sub > can be uniquely extended to a linear function.
A section Γ of: TP / G → TM such that Γ: TM → TP / G is a linear morphism of vector bundles over M, can be identified with a principal connection in P. Conversely, a principal connection as defined above gives rise to such a section Γ of TP / G.
Conversely, Lenin defined imperialism as " the highest stage of capitalism ", the era in which monopoly finance capital becomes dominant, forcing nations and corporations to compete for control over resources and markets all over the world.
Conversely, if F has characteristic zero, then given an homogeneous polynomial ƒ of degree n on V, the polarization of ƒ is a multilinear function on the n-th Cartesian product of V. The polarization is defined by
Conversely, a cooperative game can also be defined with a characteristic cost function satisfying.
where it is understood that d and ω refer to the exterior derivative and a matrix of 1-forms, respectively, acting on the components of ξ. Conversely, a matrix of 1-forms ω is a priori sufficient to completely determine the connection locally on the open set over which the basis of sections e is defined.
Conversely, this may be evidence that several distinct linguistic phenomena have been called ideophones, and that the concept therefore needs to be better defined to be useful in scientific discourse.
Conversely, since the existence of T < sup >∗∗</ sup > implies that that of T < sup >∗</ sup >, which in turn implies T is densely defined.
Conversely, any linear map defined on gives rise to an antilinear map on.
Conversely, his villainous personality tends to be that of one who is hardline or militant straight edge, exemplifying the elitist attitudes and superiority complexes — defined by Punk's common mantra during villainous-themed promos that, because he is straight edge, he is " better than you ".

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