Page 222 - Linear Algebra Done Right

Chapter 10
Trace and Determinant

Throughout this book our emphasis has been on linear maps and op-
erators rather than on matrices. In this chapter we pay more attention
to matrices as we define and discuss traces and determinants. Deter-
minants appear only at the end of this book because we replaced their
usual applications in linear algebra (the definition of the characteris-
tic polynomial and the proof that operators on complex vector spaces
have eigenvalues) with more natural techniques. The book concludes
with an explanation of the important role played by determinants in
the theory of volume and integration.

Recall that F denotes R or C.
Also, V is a finite-dimensional, nonzero vector space over F.

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