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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
In mathematics, the term linear is used in two distinct senses for two different properties: . linearity of a function (or mapping);; linearity of a polynomial.; An example of a linear function is the function defined by () = (,) that maps the real line to a line in the Euclidean plane R 2 that passes through the origin.
Linear algebra is the branch of ... is a typical example of a real ... a video presentation from 3Blue1Brown of the basics of linear algebra, with emphasis on the ...
This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector ...
A linear map is a homomorphism of vector spaces; that is, a group homomorphism between vector spaces that preserves the abelian group structure and scalar multiplication. A module homomorphism, also called a linear map between modules, is defined similarly. An algebra homomorphism is a map that preserves the algebra operations.
For example, "is a blood relative of" is a symmetric relation, because x is a blood relative of y if and only if y is a blood relative of x. Antisymmetric for all x, y ∈ X, if xRy and yRx then x = y. For example, ≥ is an antisymmetric relation; so is >, but vacuously (the condition in the definition is always false). [11] Asymmetric
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many ways for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand ...
A simple example is the way a polygon is transformed by its symmetries under reflections and rotations, which are all linear transformations about the center of the polygon. Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces , and ...
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