Linear algebra is the branch of mathematics concerning vector spaces, which often finite or countably infinite dimensional, also linear mappings between such spaces. This investigation is initially motivated by a system of linear equations containing several unknowns. These equations are naturally represented using the formalism of matrices and vectors.

Linear algebra is central to both pure and applied mathematics. As example, abstract algebra arises by relaxing the axioms of a vector space, which leading to a number of generalizations. The functional analysis studies the infinite-dimensional version of the theory of vector spaces. To combine with calculus, linear algebra facilitates the solution of linear systems of differential equations. The techniques from linear algebra are also used in analytic geometry, the engineering, the physics, the natural sciences, the computer science, the computer animation, the social sciences (particularly in economics). Linear algebra is such well-developed theory; the nonlinear mathematical models are sometimes approximated by linear ones.

Various processes from linear algebra are as well used in analytic geometry, engineering, physics, computer science, computer animation, and in economics. Because linear algebra is such a well-managed theory, nonlinear mathematical models are occasionally estimated by linear ones. We can plot complex functions by plotting commands with functions of a complex variable. By using MATLAB we can define different complex numbers in linear algebra like, Cartesian form, polar form, arithmetic with complex form, complex conjugate, real and imaginary, modulus and angle etc.

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