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In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector. More generally, a vector space may be defined by using any field instead of real numbers, such as complex numbers. Then the scalars of that vector space will be the elements of the associated field. A scalar product operation – not to be confused with scalar multiplication – may be defined on a vector space, allowing two vectors to be multiplied to produce a scalar. A vector space equipped with a scalar product is called an inner product space. The real component of a quaternion is also called its scalar part. The term is also sometimes used informally to mean a vector, matrix, tensor, or other usually "compound" value that is actually reduced to a single component. Thus, for example, the product of a 1×''n'' matrix and an ''n''×1 matrix, which is formally a 1×1 matrix, is often said to be a scalar. The term scalar matrix is used to denote a matrix of the form ''kI'' where ''k'' is a scalar and ''I'' is the identity matrix. ==Etymology== The word ''scalar'' derives from the Latin word ''scalaris'', an adjectival form of ''scala'' (Latin for "ladder"). The English word "scale" also comes from ''scala''. The first recorded usage of the word "scalar" in mathematics occurs in François Viète's ''Analytic Art'' (''In artem analyticem isagoge'') (1591):〔 〕〔 http://math.ucdenver.edu/~wcherowi/courses/m4010/s08/lcviete.pdf Lincoln Collins. Biography Paper: Francois Viete〕 :Magnitudes that ascend or descend proportionally in keeping with their nature from one kind to another may be called scalar terms. :(Latin: ''Magnitudines quae ex genere ad genus sua vi proportionaliter adscendunt vel descendunt, vocentur Scalares.'') According to a citation in the ''Oxford English Dictionary'' the first recorded usage of the term "scalar" in English came with W. R. Hamilton in 1846, referring to the real part of a quaternion: :''The algebraically real part may receive, according to the question in which it occurs, all values contained on the one scale of progression of numbers from negative to positive infinity; we shall call it therefore the scalar part.'' 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Scalar (mathematics)」の詳細全文を読む スポンサード リンク
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