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The blackboard bold letter style originated in the 1960s to distinguish bold letters from ordinary letters on a blackboard or using a typewriter; in professionally typeset documents, bold fonts were used for the same purpose. Since then, blackboard bold has gradually gained currency, and is now commonly used in mathematical printing to denote ...
A style guide, or style manual, is a set of standards for the writing and design of documents, either for general use or for a specific publication, organization or field.
For example, consider a circle of radius r. [15] The main pieces of information a program needs in order to draw this circle are An indication that what is to be drawn is a circle; the radius r; the location of the center point of the circle; stroke line style and color (possibly transparent) fill style and color (possibly transparent)
A scalar is an element of a field which is used to define a vector space.In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector.
The simplest example of a vector space over a field F is the field F itself with its addition viewed as vector addition and its multiplication viewed as scalar multiplication. More generally, all n-tuples (sequences of length n) (,, …,) of elements a i of F form a vector space that is usually denoted F n and called a coordinate space. [33]
Mathematically, a scalar field on a region U is a real or complex-valued function or distribution on U. [1] [2] The region U may be a set in some Euclidean space, Minkowski space, or more generally a subset of a manifold, and it is typical in mathematics to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order.
The term scalar component refers sometimes to scalar projection, as, in Cartesian coordinates, the components of a vector are the scalar projections in the directions of the coordinate axes.
A scalar beside a vector (either or both of which may be in parentheses) implies scalar multiplication. The two common operators, a dot and a rotated cross, are also acceptable (although the rotated cross is almost never used), but they risk confusion with dot products and cross products, which operate on two vectors.