ABSTRACT
This chapter gives a brief exposition of the versatility and applicability of linear algebra in various fields belonging to mathematical, social, physical and biological sciences, technology and engineering.
One can observe that in all recent developments there is a lot of data involved which must be streamlined and must be reduced so as to be used effectively. This can be done using tools developed using eigen values, eigen vectors, singular values and singular vectors by using eigen value decomposition and singular value decomposition.
Section 5.2 concentrates on finding the equations of curves passing through given points- which is an age old problem. In Section 5.3 Markov chains are introduced and their usefulness in solving problems in marketing and afforesting is described. Section 5.4 gives the economic models proposed by Leontief. Section 5.5 uses the modular inverse introduced in Chapter 1 and an application to cryptology is presented. Section 5.6 concentrates on computer graphics and Section 5.7 gives the basic linear algebra involved in robotics. In Section 5.8 the fact that matrices naturally arise in bioinformatics is show -cased and comparison of sequences is explained through an example using Needleman- Wunsch algorithm. Section 5.9 concentrates on one of the most useful and effective tools of linear algebra which is principal component analysis. Section 5.10 gives the basics involved in Big data and an example is given to explain the set up.
