Chapter 12 - The Gram–Schmidt Process

Abstract

This chapter reviews some definitions and results from linear algebra culminating with the Gram–Schmidt process of calculating an orthogonal and orthonormal basis. The proofs that are not included in this can be found in most linear algebra textbooks. Vectors in Rn may be given as column vectors or row vectors throughout these notes. Exercises are given to practice the linear algebra in addition to exercises that use MATLAB®. Within the exercises, functions are created to calculate bases using the Gram–Schmidt process. There are exercises to visualize random basis vectors and the resulting orthogonal and orthonormal bases in 2D and 3D.