Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars in this context. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below.

Euclidean vectors are an example of a vector space. They represent physical quantities such as forces: any two forces (of the same type) can be added to yield a third, and the multiplication of a force vector by a real multiplier is another force vector. In the same vein, but in a more geometric sense, vectors representing displacements in the plane or in three-dimensional space also form vector spaces. Vectors in vector spaces do not necessarily have to be arrow-like objects as they appear in the mentioned examples: vectors are regarded as abstract mathematical objects with particular properties, which in some cases can be visualized as arrows.

Vector Motors

Vector Motors Corporation is an American automobile manufacturer originally based in Wilmington, California. Its history can be traced to Vehicle Design Force, which was founded in 1978 by Gerald Wiegert. Vehicle production began in 1989 and ceased in the 1990s. The company was recently revived (as Vector Motors Corporation), and is currently developing a new supercar. Vector is credited by some as America's first attempt to compete with European performance car manufacturers like Ferrari, Lamborghini, and Lotus.

Nearly every car produced by the company is designated the letter "W" (for Wiegert) and a number. A letter "X" after the W (e.g. WX-8) signifies a prototype unit. The only exception to this rule is the Megatech-era M12, wherein the "M" stands for Megatech and the 12 signifies its V12 engine.

Origin

In 1971, Gerald Wiegert, fresh from college, founded a design house called Vehicle Design Force, and teamed up with Lee Brown, a well-known auto body expert in Hollywood, to create a new car called The Vector. The Vector was said to have various powerplants including a DOHC Porsche engine, and preproduction literature claimed that it would cost US$10,000 (when a new Rolls Royce Silver Shadow cost $11,500). None of these plans came to fruition, however, as Wiegert's planned production run never started. All that came of The Vector was an empty shell that was displayed at the Los Angeles Auto Show. Lee Brown left the design team shortly thereafter. The Vector was featured on the cover of Motor Trend magazine in April 1972. Wiegert renamed Vehicle Design Force to Vector Aeromotive after work began on a new project, the Vector W2.

Array data structure

In computer science, an array data structure, or simply an array, is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key. An array is stored so that the position of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called one-dimensional array.

For example, an array of 10 32-bit integer variables, with indices 0 through 9, may be stored as 10 words at memory addresses 2000, 2004, 2008, ... 2036, so that the element with index i has the address 2000 + 4 × i.

Because the mathematical concept of a matrix can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called matrices. In some cases the term "vector" is used in computing to refer to an array, although tuples rather than vectors are more correctly the mathematical equivalent. Arrays are often used to implement tables, especially lookup tables; the word table is sometimes used as a synonym of array.

Error (baseball)

In baseball statistics, an error is an act, in the judgment of the official scorer, of a fielder misplaying a ball in a manner that allows a batter or baserunner to advance one or more bases or allows an at bat to continue after the batter should have been put out.

The term error can also refer to the play during which an error was committed.

Relationship to other statistical categories

An error does not count as a hit but still counts as an at bat for the batter unless, in the scorer's judgment, the batter would have reached first base safely but one or more of the additional base(s) reached was the result of the fielder's mistake. In that case, the play will be scored both as a hit (for the number of bases the fielders should have limited the batter to) and an error. However, if a batter is judged to have reached base solely because of a fielder's mistake, it is scored as a "hit on error," and treated the same as if a batter was put out, hence lowering his batting average.

Error (linguistics)

In Applied linguistics, an error is a deviation from accepted rules of a language made by a learner of a second language. Such errors result from the learner's lack of knowledge of correct rules of the target language. A significant distinction is generally made between errors and mistakes which are not treated the same from a linguistic viewpoint. The study of learners' errors was the main area of investigation by linguists in the history of second-language acquisition research.

Definition

H. Douglas Brown has defined linguistic errors as "a noticeable deviation from the adult grammar of a native speaker, reflecting the interlanguage competence of the learner." He cites an example Does John can sing? where a preceding do auxiliary verb has been used as an error.

Difference between error and mistake

In linguistics, it is considered important to distinguish errors from mistakes. A distinction is always made between errors and mistakes where the former is defined as resulting from a learner's lack of proper grammatical knowledge, whilst the latter as a failure to utilize a known system correctly. Brown terms these mistakes as performance errors. Mistakes of this kind are frequently made by both native speakers and second language learners. However, native speakers are generally able to correct themselves quickly. Such mistakes include slips of the tongue and random ungrammatical formations. On the other hand, errors are systematic in that they occur repeatedly and are not recognizable by the learner. They are a part of the learner's interlanguage, and the learner does not generally consider them as errors. They are errors only from the perspective of teachers and others who are aware that the learner has deviated from a grammatical norm. That is, mistakes can be self-corrected with or without being pointed out to the speaker but errors cannot be self-corrected.

Error message

An error message is information displayed when an unexpected condition occurs, usually on a computer or other device. On modern operating systems with graphical user interfaces, error messages are often displayed using dialog boxes. Error messages are used when user intervention is required, to indicate that a desired operation has failed, or to relay important warnings (such as warning a computer user that they are almost out of hard disk space). Error messages are seen widely throughout computing, and are part of every operating system or computer hardware device. Proper design of error messages is an important topic in usability and other fields of human–computer interaction.

Common error messages

The following error messages are commonly seen by modern computer users:

Infamous error messages

Abort, Retry, Fail? - A notoriously confusing error message seen in MS-DOS

An example of an Error message .vbs script