From Geometry to Algebra - An Introduction to Linear Algebra

Author : Inder K. Rana, Department of Mathematics, Indian Institute of Technology, Mumbai
Publication Date : November 2003

Excerpts from the Preface:

Linear Algebra is the study of the notion of 'linearity', which arises mainly from two sources: study of geometry in the algebraic set-up, and the study of systems of linear equations which arises in the mathematical formulations of some real life problems. We shall see how these motivate one to consider the basic concepts in linear algebra such as to consider the basic concepts in linear algebra such as: vector spaces, basis, inner-product spaces, and linear transformations.

Linear Algebra has two aspects play important role in diverse branches of mathematics, physics, engineering, economics, and so on. The main aim of these notes is to present both these aspects of Linear Algebra (of course not fully, given the limited scope of these notes ). We shall try to show how abstract concepts arises out of applications and how abstract concepts can be applied in various problems.

Normally, students are taught matrices and determinants in the first introductory course in linear algebra. The notes climax in a proof of the 'Spectral Theorem', also called the 'Diagonalization Theorem' or the 'Principal Axis theorem', and some of its applications.

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