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An Introduction to the Theory of Determinants

  • James B. CarrellEmail author
Chapter

Abstract

In this chapter, we will introduce and study a remarkable function called the determinant, which assigns to an \(n\times n\) matrix A over a field \({\mathbb F}\) a scalar \(\det (A)\in {\mathbb F}\) having two remarkable properties: \(\det (A)\ne 0\) if and only if A is invertible, and if B is also in \({\mathbb F}^{n\times n}\), then \(\det (AB)=\det (A)\det (B)\). The latter property is referred to as the product formula.

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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