Vector spaceIn mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space.
DEC AlphaAlpha (original name Alpha AXP) is a 64-bit reduced instruction set computer (RISC) instruction set architecture (ISA) developed by Digital Equipment Corporation (DEC). Alpha was designed to replace 32-bit VAX complex instruction set computers (CISC) and to be a highly competitive RISC processor for Unix workstations and similar markets. Alpha is implemented in a series of microprocessors originally developed and fabricated by DEC.
Multilinear formIn abstract algebra and multilinear algebra, a multilinear form on a vector space over a field is a map that is separately -linear in each of its arguments. More generally, one can define multilinear forms on a module over a commutative ring. The rest of this article, however, will only consider multilinear forms on finite-dimensional vector spaces. A multilinear -form on over is called a (covariant) -tensor, and the vector space of such forms is usually denoted or .
Multilinear mapIn linear algebra, a multilinear map is a function of several variables that is linear separately in each variable. More precisely, a multilinear map is a function where and are vector spaces (or modules over a commutative ring), with the following property: for each , if all of the variables but are held constant, then is a linear function of . A multilinear map of one variable is a linear map, and of two variables is a bilinear map. More generally, a multilinear map of k variables is called a k-linear map.
Multilinear algebraMultilinear algebra is a branch of mathematics that expands upon the principles of linear algebra. It extends the foundational theory of vector spaces by introducing the concepts of p-vectors and multivectors using Grassmann algebras. In a vector space of dimension n, the focus is primarily on using vectors. However, Hermann Grassmann and others emphasized the importance of considering the structures of pairs, triplets, and general multi-vectors, which offer a more comprehensive perspective.
Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
Topological vector spaceIn mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar multiplication) are also continuous functions. Such a topology is called a and every topological vector space has a uniform topological structure, allowing a notion of uniform convergence and completeness.
Normed vector spaceIn mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If is a vector space over , where is a field equal to or to , then a norm on is a map , typically denoted by , satisfying the following four axioms: Non-negativity: for every ,. Positive definiteness: for every , if and only if is the zero vector.
BASIC-PLUSBASIC-PLUS is an extended dialect of the BASIC programming language that was developed by Digital Equipment Corporation (DEC) for use on its RSTS/E time-sharing operating system for the PDP-11 series of 16-bit minicomputers in the early 1970s through the 1980s. BASIC-PLUS was based on BASIC-8 for the TSS/8, itself based very closely on the original Dartmouth BASIC. BASIC-PLUS added a number of new structures, as well as features from JOSS concerning conditional statements and formatting.
Transformation (function)In mathematics, a transformation is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations.
DEC 7000 AXP and DEC 10000 AXPThe DEC 7000 AXP and DEC 10000 AXP are a series of high-end multiprocessor server computers developed and manufactured by Digital Equipment Corporation, introduced on 10 November 1992 (although the DEC 10000 AXP was not available until the following year). These systems formed part of the first generation of systems based on the 64-bit Alpha AXP architecture and at the time of introduction, ran Digital's OpenVMS AXP operating system, with DEC OSF/1 AXP available in March 1993.
PDP-8The PDP-8 is a family of 12-bit minicomputers that was produced by Digital Equipment Corporation (DEC). It was the first commercially successful minicomputer, with over 50,000 units being sold over the model's lifetime. Its basic design follows the pioneering LINC but has a smaller instruction set, which is an expanded version of the PDP-5 instruction set. Similar machines from DEC are the PDP-12 which is a modernized version of the PDP-8 and LINC concepts, and the PDP-14 industrial controller system.
Bendix G-15The Bendix G-15 is a computer introduced in 1956 by the Bendix Corporation, Computer Division, Los Angeles, California. It is about and weighs about . The G-15 has a drum memory of 2,160 29-bit words, along with 20 words used for special purposes and rapid-access storage. The base system, without peripherals, cost 49,500.Aworkingmodelcostaround60,000 (over 500,000bytoday′sstandards).Itcouldalsoberentedfor1,485 per month. It was meant for scientific and industrial markets. Martha Reeves (anchorite)Martha Reeves (born 1941) is a vowed Anglican solitary (or anchorite), with Rowan Williams, the former Archbishop of Canterbury, as bishop-protector. A graduate of the Madeira School (Class of 1959), she is also a Stanford-educated professor of theology who has written numerous articles and books under the name "Maggie Ross" as well as translated a number of Carthusian Novice Conferences. Reeves, at one time Desmond Tutu's spiritual director, was Bell Distinguished Professor in Anglican and Ecumenical Studies appointed to the Department of Philosophy and Religion, Kendall College of Arts and Sciences, The University of Tulsa.
Ed Roberts (computer engineer)Henry Edward Roberts (September 13, 1941 – April 1, 2010) was an American engineer, entrepreneur and medical doctor who invented the first commercially successful personal computer in 1974. He is most often known as "the father of the personal computer." He founded Micro Instrumentation and Telemetry Systems (MITS) in 1970 to sell electronics kits to model rocketry hobbyists, but the first successful product was an electronic calculator kit that was featured on the cover of the November 1971 issue of Popular Electronics.
Graded vector spaceIn mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct sum of vector subspaces, generally indexed by the integers. For "pure" vector spaces, the concept has been introduced in homological algebra, and it is widely used for graded algebras, which are graded vector spaces with additional structures. Let be the set of non-negative integers.
Dimension (vector space)In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension. For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined. We say is if the dimension of is finite, and if its dimension is infinite.
Geometric transformationIn mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations).
Ohio ScientificOhio Scientific, Inc. (OSI, originally Ohio Scientific Instruments, Inc.), was a privately owned American computer company based in Ohio that built and marketed computer systems, expansions, and software from 1975 to 1986. Their best-known products were the Challenger series of microcomputers and Superboard single-board computers. The company was the first to market microcomputers with hard disk drives in 1977. The company was incorporated as Ohio Scientific Instruments in Hiram, Ohio, by husband and wife Mike and Charity Cheiky and business associate Dale A.
