Mathematical Methods

3

Real and Complex Matrices

3.1 Introduction

A matrix with real entries is called a real matrix. We have studied various types of real matrices and their properties. Matrices with complex entries are also important in the study of quantum mechanics, quadratic forms, etc. We now consider three classes of real square matrices—symmetric, skew-symmetric and orthogonal matrices and also their counterparts with complex elements which are important in applications. But first we define certain terms.

3.2 Orthogonal/Orthonormal System of Vectors

3.2.1 Norm of a Vector

The norm of a vector X denoted by || X || is defined by

If

E.g.

3.2.2 Orthonormal ...