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Conversely, any linear map defined on gives rise to an antilinear map on.
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Conversely and any
Conversely, let G be any polynomial such that Af.
Conversely, any algebra whose associator is alternating is clearly alternative.
Conversely, any algebra for which this is true is clearly alternative.
Conversely, a subset R defines a binary function if and only if, for any x in X and y in Y, there exists a unique z in Z such that ( x, y, z ) belongs to R.
Conversely the equilibrium position is said to be " far to the left " if hardly any product is formed from the reactants.
* The spectrum of any bounded linear operator on a Banach space is a nonempty compact subset of the complex numbers C. Conversely, any compact subset of C arises in this manner, as the spectrum of some bounded linear operator.
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, corresponding to any partition of X, there exists an equivalence relation ~ on X.
Conversely, any surjection between sets determines a partition on its domain, the set of preimages of singletons in the codomain.
Conversely, Derek Bickerton and others argue that the advent of abstract words provided a mental basis for analyzing higher-order relations, and that any communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language.
Conversely any planar graph can be formed from a map in this way.
Conversely, a person may feel like he belongs to one state without having any legal relationship to it.
Conversely, the interior of the box has a constant, zero potential energy .< ref > Actually, any constant, finite potential can be specified within the box.
Conversely, extremely thin jewelry can cause the same tearing in what is commonly referred to as the " cheese cutter effect ", either during sudden torsion or over a long period of wearing, especially if the thin jewelry bears any weight.
Conversely, any Hermitian positive semidefinite matrix M can be written as M = A < sup >*</ sup > A ; this is the Cholesky decomposition.
Conversely, if a double sharp were added to any other note not containing a sharp or flat as indicated by the key signature then the note will be raised two semitones or a whole step with respect to the chromatic scale.
Conversely in rings with unity, any simple left R module arises this way.
Conversely, supplementation with L-phenylalanine, L-tyrosine, L-DOPA, or any of the cofactors will increase their respective concentrations.
Conversely, any choice of μ, full rank matrix U, and positive diagonal entries Λ < sub > i </ sub > yields a non-singular multivariate normal distribution.
Conversely, in the absence of spatial continuity can take any value.
Conversely, the influence of the data at any given point on the initial line propagates with the finite velocity c: there is no effect outside a triangle through that point whose sides are characteristic curves.
Conversely, given any harmonic function in two dimensions, it is the real part of an analytic function, at least locally.
Conversely, if the Turing Machine is expected polynomial-time ( for any given x ), then a considerable fraction of the runs must be polynomial-time bounded, and the coin sequence used in such a run will be a witness.
It is a fact that the ring is a principal ideal ring ; that is, for any ideal I in, there exists an integer n in I such that every element of I is a multiple of n. Conversely, the set of all multiples of an arbitrary integer n is necessarily an ideal, and is usually denoted by ( n ).
Conversely and linear
Conversely it may generate too many points in areas where the curve is close to linear.
Conversely, any affine linear transformation extends uniquely to a projective linear transformations, so the affine group is a subgroup of the projective group.
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.
Conversely, any sequence that satisfies a linear recurrence determines a rational function when used as the coefficients of a Taylor series.
A section Γ of dπ: 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, by the Riesz representation theorem, each positive linear form on arises as integration with respect to a Radon measure and is thus a continuous positive linear form on.
Conversely, the fractional linear transformations are the only functions with this property.
Conversely, given any Lie algebra with a direct sum decomposition satisfying these three conditions, the linear map σ, equal to the identity on and minus the identity on, is an involutive automorphism.
Conversely, any uniformly continuous semigroup is necessarily of this form for some bounded linear operator A.
Conversely, the relationship between and is linear, and so linear regression is used to estimate the latent heat.
Conversely, given an SL ( n )- structure, one can recover a volume form by imposing () for the special linear frames and then solving for the required n-form ω by requiring homogeneity in its arguments.
Conversely and map
Conversely, a particular map between particular objects may be called an unnatural isomorphism ( or " this isomorphism is not natural ") if the map cannot be extended to a natural transformation on the entire category.
Conversely, a normal subgroup of index p determines a non-trivial map to up to a choice of " which coset maps to which shows that this map is a bijection.
Suppose S is an immersed submanifold of M. If the inclusion map i: S → M is closed then S is actually an embedded submanifold of M. Conversely, if S is an embedded submanifold which is also a closed subset then the inclusion map is closed.
Conversely, any map Φ of this form is a quantum operation provided
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.
Conversely, if either of these last two expressions is defined, then so is the other ( and again they are equal ).
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, 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, symmetric tensors are defined as invariants: given the natural action of the symmetric group on the tensor algebra, the symmetric tensors are the subspace on which the symmetric group acts trivially.
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, 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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