Linear algebra
Linear algebra is a share of mathematics, researching linear spaces, usually with a finite or countable number of dimensions, as well as the linear images (the linear categories) between such spaces. This includes the study of lines, planes, and subspaces, but also touches on properties common to all linear spaces.
Linear algebra
The set of points with coordinates satisfying a given linear equation form hyperplane in n-dimensional space. The conditions under which multiple of n hyperplanes intersect at a single point. They are one of the main goals of research in linear algebra. These studies arise initially with the aim of solving systems of linear equations with a few unknowns that are easy to represent in the form of matrices and vectors.[1][2][3]
Linear algebra
Linear algebra is central to both pure and applied mathematics. For example, abstract algebra arises by removing some of the axioms about linear spaces, which allows for significant generalizations of the derivations of linear algebra. Functional analysis studies the theory of linear spaces in an infinite number of dimensions. In combination with mathematical analysis linear algebra makes it possible to solve linear systems of differential equations.
Linear algebra
Methods of linear algebra are also used in analytic geometry, the technique, physics and the rest natural Science, informatics and social sciences, mostly in the economy. Since the apparatus of linear algebra is very well developed, sometimes nonlinear mathematical models are approximated by linear ones.
- Linear algebra
- Analytical geometry