An Introduction to the Theory of Determinants

James B. Carrell ()
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James B. Carrell: University of British Columbia, Department of Mathematics

Chapter Chapter 5 in Groups, Matrices, and Vector Spaces, 2017, pp 113-134 from Springer

Abstract: 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.

Date: 2017
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DOI: 10.1007/978-0-387-79428-0_5

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