A Practical Approach To Linear Algebra

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, solution of coupled differential equations, determination of a circle passing through three given points, as well as many other problems in mathematics, physics, and engineering. Confusingly, linear algebra is not actually an algebra in the technical sense of the word algebra. Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, and the social sciences. Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear ones. The field of Linear Algebra is more beautiful and more fundamental than its rather dull name may suggest. More beautiful because it is full of powerful ideas that are quite unlike those normally emphasized in a linear algebra course in a mathematics department. The subject matter has been discussed in such a simple way that the students will find no difficulty to understand it. The students should first try to understand the theorems and then they should try to solve the questions independently.