Page 174 - Linear Algebra Done Right

Chapter 8
Operators on

Complex Vector Spaces

In this chapter we delve deeper into the structure of operators on
complex vector spaces. An inner product does not help with this ma-
terial, so we return to the general setting of a finite-dimensional vector
space (as opposed to the more specialized context of an inner-product
space). Thus our assumptions for this chapter are as follows:

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

Some of the results in this chapter are valid on real vector spaces,
so we have not assumed that V is a complex vector space. Most of the
results in this chapter that are proved only for complex vector spaces
have analogous results on real vector spaces that are proved in the next
chapter. We deal with complex vector spaces first because the proofs
on complex vector spaces are often simpler than the analogous proofs
on real vector spaces.
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