O'Reilly logo

Linear Algebra by Promode Kumar Saikia

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

7

Bilinear Forms

7.1 INTRODUCTION

In analytic geometry for ℝ2 and ℝ3 (or in vector analysis), natural geometric concepts such as length, distance and perpendicularity are introduced through the dot product or inner product of two vectors. The idea of bilinear forms generalizes the dot product, and provides the proper setting for concepts of length, distance and perpendicularity even in abstract vector spaces. Not surprisingly, these ideas turn out to be powerful geometric tools in advanced mathematics as well as in solving diverse applied problems. This chapter is a brief introduction to the elementary theory of bilinear forms.

7.2 BASIC CONCEPTS

We begin with a brief review of the definition of the dot product in analytic geometry. In ℝ2, for ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required