COCONET's bitmap and vector graphics and support for multiple type fonts were inspired by the PLATO system, and the graphics capabilities were based on what was available in the Borland BGI graphics library.

A vector of this type is known as a convex combination of.

There is a product rule of the following type: if is a scalar valued function and F is a vector field, then

Representation theory also depends heavily on the type of vector space on which the group acts.

One must also consider the type of field over which the vector space is defined.

* Neutral vector ( statistics ), a multivariate random variable is neutral if it exhibits a particular type of statistical independence seen when considering the Dirichlet distribution

This more general type of spatial vector is the subject of vector spaces ( for bound vectors ) and affine spaces ( for free vectors ).

Tensors are another type of quantity that behave in this way ; in fact a vector is a special type of tensor.

A complex instruction type that has become particularly popular recently is the SIMD or Single-Instruction Stream Multiple-Data Stream operation or vector instruction, an operation that performs the same arithmetic operation on multiple pieces of data at the same time.

All of these developments have been oriented toward support for real-time graphics, and are therefore oriented toward processing in two, three, or four dimensions, usually with vector lengths of between two and sixteen words, depending on data type and architecture.

Unlike SSE2, AltiVec supports a special RGB " pixel " data type, but it does not operate on 64-bit double precision floats, and there is no way to move data directly between scalar and vector registers.

However, AltiVec provides a much more complete set of " horizontal " operations that work across all the elements of a vector ; the allowable combinations of data type and operations are much more complete.

There are also overloaded intrinsic functions such as "" that emit the appropriate op code based on the type of the elements within the vector, and very strong type checking is enforced.

In the language of schemes, finite type modules are interpreted as coherent sheaves, or generalized finite rank vector bundles.

The ES is a highly parallel vector supercomputer system of the distributed-memory type, and consisted of 160 processor nodes connected by Fat-Tree Network.

The same type of vector pipelines works together by a single vector instruction and pipelines of different types can operate concurrently.

) But if a mathematical model — essentially, a vector graphic — is declared to be the official definition of the part, then any amount of " scaling the drawing " can make sense ; there may still be an error in the model, in the sense that what was intended is not depicted ( modeled ); but there can be no error of the " not to scale " type — because the mathematical vectors and curves are replicas, not symbols, of the part features.

It is a type of linear classifier, i. e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector describing a given input.

In C ++, the standard way of accessing AltiVec support is mutually exclusive with use of the Standard Template Library < code > vector <></ code > class template due to the treatment of " vector " as a reserved word when the compiler does not implement the context sensitive keyword version of vector.

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 ).

His hemoglobin levels are presently stable at 9 to 10 g / dL and about a third of the hemoglobin contains the form introduced by the viral vector.

To allow this anisotropic structure, a dimensionless unit vector n called the director, is introduced to represent the direction of preferred orientation of molecules in the neighborhood of any point.

The first modern and more precise definition of a vector space was introduced by Peano in 1888 ; by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged.

: This release introduced support for vector graphics.

, spinors are elements of a complex vector space introduced to expand the notion of spatial vector.

Once tangent spaces have been introduced, one can define vector fields, which are abstractions of the velocity field of particles moving on a manifold.

In the process he introduced the magnetic vector potential which was later shown to be equivalent to the underlying mechanism proposed by Faraday.

Gibbs introduced the now common notation for the dot product and the cross product of two vectors, and he was largely responsible for the development of the vector calculus techniques still used today in electrodynamics and fluid mechanics.

* It introduced a vector base register ( VBR ), which allowed the vector jump table to be anywhere in RAM.

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.

Transductive support vector machines were introduced by Vladimir N. Vapnik in 1998.

E. coli is one of the most widely used expression hosts, and DNA is normally introduced in a plasmid expression vector.

This revolutionary theoretical framework is based on a probabilistic interpretation of states, and evolution and measurements in terms of self-adjoint operators on an infinite dimensional vector space ( Hilbert space, introduced by David Hilbert ).

In particular, if v = e < sub > j </ sub > is the jth coordinate vector then ∂< sub > v </ sub > f is the partial derivative of f with respect to the jth coordinate function, i. e., ∂ f / ∂ x < sup > j </ sup >, where x < sup > 1 </ sup >, x < sup > 2 </ sup >, ... x < sup > n </ sup > are the coordinate functions on U. By their very definition, partial derivatives depend upon the choice of coordinates: if new coordinates y < sup > 1 </ sup >, y < sup > 2 </ sup >, ... y < sup > n </ sup > are introduced, then

The CPUs in these models introduced vector gather / scatter memory reference instructions to the product line.

In 1940, Léon Rosenfeld — and before him Wolfgang Pauli — introduced what he called a ‘ local variation ’ of a geometric object induced by an infinitesimal transformation of coordinates generated by a vector field.

The last part of VC theory introduced a well-known learning algorithm: the support vector machine.

Classical gene therapy is the approach which delivers genes, via a modified virus or " vector " to the appropriate target cells with a goal of attaining optimal expression of the new, introduced gene.

Adobe Illustrator, a vector drawing program based on the Bézier curve introduced in 1987 and Adobe Photoshop, written by brothers Thomas and John Knoll in 1990 were developed for use on MacIntosh computers.