27-06-2017, 03:16 PM
Linear algebra is the branch of mathematics relative to vector spaces and linear assignments between these spaces. It includes the study of lines, planes and subspaces, but also deals with the properties common to all vector spaces.
The set of points with coordinates satisfying a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect at a single point is an important focus of study in linear algebra. Such research is initially motivated by a system of linear equations containing several unknowns. Such equations are represented naturally using the formalism of matrices and vectors.
Linear algebra is central to both pure mathematics and applied mathematics. For example, abstract algebra arises by relaxing the axioms of a vector space, giving rise to a series of generalizations. Functional analysis studies the version of the infinite dimension of the theory of vector spaces. Combined with the calculation, linear algebra facilitates the solution of linear systems of differential equations.
Linear algebra techniques are also used in analytical geometry, engineering, physics, natural sciences, computer science, computer animation, advanced facial recognition algorithms and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models.