Linear Algebra: Theory and Applications, 2nd Edition

CHAPTER FOURDeterminants

4.1 DETERMINANTS: INTRODUCTION

I was x years old in the year x².

—AUGUSTUS DE MORGAN (1806–1871), RESPONDING TO THE QUESTION OF HOW OLD HE WAS

To speak algebraically, Mr. M. is execrable, but Mr. C. is x plus 1 - ecrable.

—EDGAR ALLAN POE (1809–1849)

Properties of Determinants

With every square matrix there is associated a real number called the determinant of that matrix. The notation used here is Det(A) or Det A for the determinant of A. There are various ways to present postulates for determinants from which all other properties follow. We have chosen to start with the following three basic properties of determinants because they lead directly to their efficient calculation.

PROPERTIES OF DETERMINANTS

I. The determinant ...