The technique requires that all vectors are augmented with a " 1 " at the end, and all matrices are augmented with an extra row of zeros at the bottom, an extra column — the translation vector — to the right, and a " 1 " in the lower right corner.

Microwave Early Warning ( MEW ) radar, another technique pioneered by Quesada, was also used by XIX TAC as an air traffic control radar to both cover against Luftwaffe attacks and to vector flights already in the air to new sites.

By some chosen technique such as ordinary least squares, a vector is chosen as an estimate of, and the estimate of the vector, denoted, is computed as

The vector technique was first fully exploited in 1976 by the famous Cray-1.

This allowed a batch of vector instructions themselves to be pipelined, a technique they called vector chaining.

* Space vector modulation, in power electronics, a modulating technique to give power to a load

Moreover, the technique can be further generalized in a straightforward way to also include an entropy constraint for vector data.

A key feature of this approach allowed for the components of the vector cross product ( v, xdv ,/ dt ) to be used as the basic autopilot rate signals-a technique that became known as " cross-product steering.

This technique cannot be generalised to more than one color, or to vector shapes.

In 1930, following the 1909 discovery of Charles Nicolle that lice were the vector of epidemic typhus and on the work for the vaccine for the closely related Rocky Mountain Spotted Fever, Weigl took the next step and developed a technique to produce the vaccine by growing infected lice and crushing them into a vaccine paste.

This rendering technique allowed for much more detailed and realistic terrain compared to simulations based on vector graphics at that time.

The ECMWF model, the Ensemble Prediction System, uses singular vectors to simulate the initial probability density, while the NCEP ensemble, the Global Ensemble Forecasting System, uses a technique known as vector breeding .< ref name =" Toth ">

TwinVQ ( transform-domain weighted interleave vector quantization ) is an audio compression technique developed by Nippon Telegraph and Telephone Corporation ( NTT ) Human Interface Laboratories ( now Cyber Space Laboratories ) in 1994.

This technique involves each vector operation being done for a size less than or equal to the maximum vector length on a given vector machine.

In molecular biology, subcloning is a technique used to move a particular gene of interest from a parent vector to a destination vector in order to further study its functionality.

Vexel is a neologism for an entirely pixel-based form of raster art that imitates the visual appearance of vector graphics technique ( i. e. sharp-edged lines and areas of flat colour or smooth gradient fills ).

Ben Woolley says " exels were originally meant to involve a vector technique, not any particular aesthetic style.

The ECMWF model, the Ensemble Prediction System, uses singular vectors to simulate the initial probability density, while the NCEP ensemble, the Global Ensemble Forecasting System, uses a technique known as vector breeding .< ref name =" Toth ">

It is clear that each vector in the range of Af is in Af for if **ya is in the range of Af, then Af and so Af because Af is divisible by the minimal polynomial P.

From these results, one sees that the study of linear operators on vector spaces over an algebraically closed field is essentially reduced to the study of nilpotent operators.

In the primary decomposition theorem, it is not necessary that the vector space V be finite dimensional, nor is it necessary for parts ( A ) and ( B ) that P be the minimal polynomial for T.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

If the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.

If T is the total `` length '' of the process, its feed state may be denoted by a vector p(T) and the product state by p(Q).

The Asteroids arcade machine is a vector game.

Many theorems which are provable using choice are of an elegant general character: every ideal in a ring is contained in a maximal ideal, every vector space has a basis, and every product of compact spaces is compact.

** On every infinite-dimensional topological vector space there is a discontinuous linear map.

For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces.

In the context of abstract algebra, for example, a mathematical object is an algebraic structure such as a group, ring, or vector space.

* In linear algebra, an endomorphism of a vector space V is a linear operator V → V. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL ( V ).

It is similar to distance vector routing.

Path vector routing is discussed in RFC 1322 ; the path vector routing algorithm is somewhat similar to the distance vector algorithm in the sense that each border router advertises the destinations it can reach to its neighboring router.

For vector wave equations, such as the ones describing electromagnetic radiation or waves in an elastic solid, the solution for a homogeneous medium is similar: the scalar amplitude A < sub > o </ sub > is replaced by a constant vector A < sub > o </ sub >.

An entirely new phenomenology of high energy collisions has resulted, in which strong interaction phenomena are dominated by the exchange of the quanta of the strong force, the gluons, particles which are similar to the intermediate vector bosons, although, like the photons, they are apparently massless.

None of these techniques, however, makes any difference to the basic principles of EIGRP, which exchanges a vector of distances to each known destination network without full knowledge of the network topology, and, as a matter of fact, similar techniques have been used in other distance-vector protocols ( notably DSDV, AODV and Babel ).

In the early and mid-1980s Japanese companies ( Fujitsu, Hitachi and Nippon Electric Corporation ( NEC ) introduced register-based vector machines similar to the Cray-1, typically being slightly faster and much smaller.

A similar cloning vector called a PAC has also been produced from the bacterial P1-plasmid.

A similar transformation law characterizes vector fields in physics: specifically, a vector field is a specification of n functions in each coordinate system subject to the transformation law () relating the different coordinate systems.

Using the unit vector defined before, the angular velocity vector may be written in a manner similar to that for two dimensions:

They planned on producing a machine very similar in architecture to the Cray Research vector processor machines, with a somewhat lower performance, but with a much better price / performance ratio.

During subsequent reflections the direction of this polarization vector is changed but it is changed differently for each path in a manner similar to a Foucault pendulum.

Adhémar Jean Claude Barré de Saint-Venant developed a vector calculus similar to that of Grassmann which he published in 1845.

These implemented an instruction set similar to the Fujitsu VP2000 vector supercomputer and had a nominal performance of 200 megaflops on double precision arithmetic and double that on single precision.

WMF has the potential to provide vector previews, similar to PICT on the Mac.

Decryption is similar, start with the initialization vector, encrypt, and XOR the high bits of the result with x bits of the ciphertext to produce x bits of plaintext.

* Extended Vector Animation, a web-based vector graphic file format, similar to the Macromedia Flash format

Another, similar, alternative is the relativistic modified gravity ( MOG ) theory, also called scalar – tensor – vector gravity ( STVG ), of John Moffat.

This error will be returned to shortly and eliminated from the new forward vector ; but first, the backwards vector must be extended in a similar ( albeit reversed ) fashion.

Free abelian groups have very nice properties which make them similar to vector spaces and allow a general abelian group to be understood as a quotient of a free abelian group by " relations ".