System of linear equationsIn mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by the ordered triple since it makes all three equations valid. The word "system" indicates that the equations should be considered collectively, rather than individually.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
Red-figure potteryRed-figure vase painting is one of the most important styles of figural Greek vase painting. It developed in Athens around 520 BCE and remained in use until the late 3rd century BCE. It replaced the previously dominant style of black-figure vase painting within a few decades. Its modern name is based on the figural depictions in red color on a black background, in contrast to the preceding black-figure style with black figures on a red background. The most important areas of production, apart from Attica, were in Southern Italy.
Black-figure potteryBlack-figure pottery painting, also known as the black-figure style or black-figure ceramic (), is one of the styles of painting on antique Greek vases. It was especially common between the 7th and 5th centuries BCE, although there are specimens dating as late as the 2nd century BCE. Stylistically it can be distinguished from the preceding orientalizing period and the subsequent red-figure pottery style. Figures and ornaments were painted on the body of the vessel using shapes and colors reminiscent of silhouettes.
Additive mapIn algebra, an additive map, -linear map or additive function is a function that preserves the addition operation: for every pair of elements and in the domain of For example, any linear map is additive. When the domain is the real numbers, this is Cauchy's functional equation. For a specific case of this definition, see additive polynomial. More formally, an additive map is a -module homomorphism. Since an abelian group is a -module, it may be defined as a group homomorphism between abelian groups.
