Determinants of Matrices

Abstract

The determinant is a map that assigns to every square matrix $$A \in R^{n,n}$$A∈Rn,n, where R is a commutative ring with unit, an element of R. This map has very interesting and important properties. For instance it yields a necessary and sufficient condition for the invertibility of $$A \in R^{n,n}$$A∈Rn,n. Moreover, it forms the basis for the definition of the characteristic polynomial of a matrix in Chap. 8.