This final chapter is a collection of a few topics which, we believe, every student of linear algebra should be acquainted with. The topics chosen are examples of aesthetically pleasing mathematics which also have wide-ranging applications.
Real quadratic forms and real symmetric matrices constitute one such topic. By their very nature, such forms and matrices are essential in more applications than any other concept from linear algebra. We had briefly touched on real quadratic forms and real symmetric matrices in earlier chapters; in Section 9.3, we present an exhaustive treatment of several applications such as classifications of conics and quadrics and solutions to the problems of constrained optimization ...