Advertisement

# Determinants

• Thomas Banchoff
• John Wermer
Part of the Undergraduate Texts in Mathematics book series (UTM)

## Abstract

Let A be a linear transformation with matrix $$\left( {\begin{array}{*{20}{c}} a\\ c \end{array}\;\begin{array}{*{20}{c}} b\\ d \end{array}} \right)$$. The quantity
$$ad\; - \;bc$$
is called the determinant of the matrix $$\left( {\begin{array}{*{20}{c}} a\\ c \end{array}\;\begin{array}{*{20}{c}} b\\ d \end{array}} \right)$$ and is denoted
$$\left| {\begin{array}{*{20}{c}} a\\ c \end{array}\;\;\;\begin{array}{*{20}{c}} b\\ d \end{array}} \right|\;{\rm{.}}$$
(1)
Expressed in these terms, Theorem 2.4 states that A has an inverse if and only if $$\left| {\begin{array}{*{20}{c}} a\\ c \end{array}\;\;\;\begin{array}{*{20}{c}} b\\ d \end{array}} \right|\; \ne \;{\rm{0}}{\rm{.}}$$ We shall see that the determinant gives us further information about the behavior of A.

## Preview

Unable to display preview. Download preview PDF.

## Copyright information

© Springer-Verlag New York, Inc. 1992

## Authors and Affiliations

• Thomas Banchoff
• 1
• John Wermer
• 1
1. 1.Department of MathematicsBrown UniversityProvidenceUSA