Baidu Encyclopedia version

Linear algebra is a branch of mathematics. Its research objects are vectors, vector spaces (or linear spaces), linear transformations and linear systems of finite dimensions. Vector space is an important topic in modern mathematics; therefore, linear algebra is widely used in abstract algebra and functional analysis; by analytic geometry, linear algebra can be specifically represented. The theory of linear algebra has been generalized to operator theory. Since nonlinear models in scientific research can usually be approximated as linear models, linear algebra is widely used in the natural sciences and social sciences.

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Wikipedia version

Linear algebra is a mathematical branch of a linear equation, such as

{\ displaystyle a_ {1} x_ {1} + \ cdots + a_ {n} x_ {n} = b,}

Linear function such as

{\ displaystyle(x_ {1},\ ldots,x_ {n})\ mapsto a_ {1} x_ {1} + \ ldots + a_ {n} x_ {n},}

And they are represented by matrices and vector spaces. Linear algebra is at the heart of almost all areas of mathematics. For example, linear algebra is the basis in modern representations of geometry, including the use of defining basic objects such as lines, planes, and rotations. In addition, functional analysis can basically be seen as the application of linear algebra in function space. Linear algebra is also used in most scientific and engineering fields because it allows modeling of many natural phenomena and using them to perform efficient calculations. For nonlinear systems that cannot be modeled by linear algebra, linear algebra is often used as a first order approximation.

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