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For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. [3] [4] In category theory, a map may refer to a morphism. [2] The term transformation can be used interchangeably, [2] but transformation often refers to a function from a set to itself.
They settled on five themes: location, place, relationships within places (later changed to human-environment interaction), relationships between places (later shortened to movement), and region. [4] The themes were not a "new geography" but rather a conceptual structure for organizing information about geography. [1]
In linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements as a solution.. More precisely, if , …, are elements of a (left) module M over a ring R (the case of a vector space over a field is a special case), a relation between , …, is a sequence (, …,) of elements of R such that
Lineations in structural geology are linear structural features within rocks. [1] There are several types of lineations, intersection lineations, crenulation lineations, mineral lineations and stretching lineations being the most common. Lineation field measurements are recorded as map lines with a plunge angle and azimuth.
Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points. This results in a continuous curve, with a discontinuous derivative (in general), thus of differentiability class.
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).
Then, a type of spatial relation can be expressed by the class of the objects that participate in the relation: point-point relations: ... point-line relations: point-area relations: line-line relations: line-area relations: area-area relations: More complex modeling schemas can represent an object as a composition of simple sub-objects.
In the above figure, P 1 has a winning strategy as follows: N 1 points only to nodes N 2 and N 3. Thus P 1 's first move must be one of these two choices. P 1 chooses N 2 (if P 1 chooses N 3, then P 2 will choose N 9 as that is the only option and P 1 will lose). Next P 2 chooses N 4 because it is the only remaining choice. P 1 now chooses N 5 ...