The treaty was negotiated via subspace radio, again with no visual contact.

; Limited communication: A central theme to Traveller is that there is no form of faster-than-light information transfer – meaning no ansible, subspace radio or hyper-wave communication technology is available.

Due to the lack of use of visual communications, the two races have never seen each other and only communicated over subspace radio.

Later in that century, Humans fought an interstellar nuclear war with the Romulans, a war that ended with the negotiation of a peace treaty by subspace radio.

While travelling the Delta Quadrant, Voyager is contacted by Starfleet Command via an improved subspace radio amplifier.

Using the enhanced subspace radio relay established by Starfleet, Voyager transmits the Doctor's programme back to the Alpha Quadrant, a journey of 30, 000 light years.

The best known Krylov subspace methods are the Arnoldi, Lanczos, Conjugate gradient, GMRES ( generalized minimum residual ), BiCGSTAB ( biconjugate gradient stabilized ), QMR ( quasi minimal residual ), TFQMR ( transpose-free QMR ), and MINRES ( minimal residual ) methods.

Bombieri is also known for his pro bono service on behalf of the mathematics profession, e. g. for serving on external review boards and for peer-reviewing extraordinarily complicated manuscripts ( like the papers of John Nash on embedding Riemannian manifolds and of Per Enflo on the invariant subspace problem ).

Volition also used the term " FreeSpace " in the game to initially describe what became later known as subspace.

More generally, if W is a linear subspace of a ( possibly infinite dimensional ) vector space V then the codimension of W in V is the dimension ( possibly infinite ) of the quotient space V / W, which is more abstractly known as the cokernel of the inclusion.

In the field of mathematics known as functional analysis, the invariant subspace problem for a complex Banach space H of dimension > 1 is the question whether

DIIS ( direct inversion in the iterative subspace or direct inversion of the iterative subspace ), also known as Pulay mixing, is an extrapolation technique.

Therefore MUSIC beamformer is also known as subspace beamformer.

Theoretical results have shown that convergence improves with an increase in the Krylov subspace dimension n. However, an a-priori value of n which would lead to optimal convergence is not known.

As a linear subspace of, the entire code C ( which may be very large ) may be represented as the span of a minimal set of codewords ( known as a basis in linear algebra ).

If the largest eigenvalue is multiple, then will converge to a vector in the subspace spanned by the eigenvectors associated with those largest eigenvalues. Having found the first eigenvector / value, one can then successively restrict the algorithm to the null space of the known eigenvectors to get the second largest eigenvector / values and so on.

If X is a topological space and M is a complete metric space, then the set C < sub > b </ sub >( X, M ) consisting of all continuous bounded functions ƒ from X to M is a closed subspace of B ( X, M ) and hence also complete.

Separable metrizable spaces can also be characterized as those spaces which are homeomorphic to a subspace of the Hilbert cube, i. e. the countably infinite product of the unit interval ( with its natural subspace topology from the reals ) with itself, endowed with the product topology.

* Every closed subgroup of a profinite group is itself profinite ; the topology arising from the profiniteness agrees with the subspace topology.

Over the course of the series, the crew of Voyager found a number of ways to shorten their journey by many decades, thanks to shortcuts ( in the episodes " Night ", " Q2 "), technology boosts (" The Voyager Conspiracy ", " Dark Frontier ", " Timeless ", " Hope and Fear "), subspace corridors (" Dragon's Teeth "), and a mind-powered push from a powerful former shipmate (" The Gift ").

In Star Trek, tractor beams are imagined to work by placing a target in the focus of a subspace / graviton interference pattern created by two beams from an emitter.

Let V and W be vector spaces ( or more generally modules ) and let T be a linear map from V to W. If 0 < sub > W </ sub > is the zero vector of W, then the kernel of T is the preimage of the zero subspace

It works by encoding values from a multidimensional vector space into a finite set of values from a discrete subspace of lower dimension.

More explicitly, an injective continuous map f: X → Y between topological spaces X and Y is a topological embedding if f yields a homeomorphism between X and f ( X ) ( where f ( X ) carries the subspace topology inherited from Y ).

If X is a Tychonoff space then the map from X to its image in βX is a homeomorphism, so X can be thought of as a ( dense ) subspace of βX.

* The map from X to its image in βX is a homeomorphism to an open subspace if and only if X is locally compact Hausdorff.

A linear subspace is usually called simply a subspace when the context serves to distinguish it from other kinds of subspaces.

If it is not, then it can be completed: one can find an essentially unique complete topological ring S which contains R as a dense subring such that the given topology on R equals the subspace topology arising from S.

Note however that there is no correspondence with regards to perpendicular planes, because vectors in subspaces start from the origin ( definition of vector subspace ).

Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.

During the war against the Shivans, a last-ditch attack in subspace saves the planet from destruction, but at the cost of collapsing the FTL node that allows access to the system.

Many bottoms require aftercare while returning from subspace.

Now consider the space X which consists of the union of the two intervals and of R. The topology on X is inherited as the subspace topology from the ordinary topology on the real line R. In X, the set is clopen, as is the set.

For instance, the completion of a metric space M involves an isometry from M into M, a quotient set of the space of Cauchy sequences on M. The original space M is thus isometrically isomorphic to a subspace of a complete metric space, and it is usually identified with this subspace.

A bounded linear operator S from X to Y is strictly singular when its restriction to any infinite dimensional subspace X < sub > 0 </ sub > of X fails to be an into isomorphism, that is:

The destruction of the Lucifer in the subspace between the Sol and Delta Serpentis jump nodes marks a twist in the ending ; the subspace corridor is destroyed and Sol is cut off from the Terran survivors outside who must face the possibility of meeting the Shivans again.

An " urgent subspace message " on the Star Trek 2. 0 Hailing Frequencies e-newsletter stated that Star Trek: The Next Generation 2. 0 was scheduled for a " refit ".

The problems of the Hobus supernova being so devastating to other solar systems is addressed in the computer game Star Trek Online, by declaring the blast to have " traveled through subspace ".

* In Star Trek: Voyager, a fictional spacecraft named Ares IV ( not to be confused with the actual Ares IV rocket ) is launched in early 2032 and trapped inside a graviton ellipse, a huge body of subspace energy travelling through the galaxy.

* The USS Voyager in Star Trek: Voyager finds a species with subspace teleport technology able to cross thousands of lightyears.

In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower dimensional subspace, called the Poincaré section, transversal to the flow of the system.