Page 88 - Linear Algebra Done Right

Chapter 5
Eigenvalues and Eigenvectors

In Chapter 3 we studied linear maps from one vector space to an-
other vector space. Now we begin our investigation of linear maps from
a vector space to itself. Their study constitutes the deepest and most
important part of linear algebra. Most of the key results in this area
do not hold for infinite-dimensional vector spaces, so we work only on
finite-dimensional vector spaces. To avoid trivialities we also want to
eliminate the vector space {0} from consideration. Thus we make the
following assumption:

Recall that F denotes R or C.
Let’s agree that for the rest of the book
V will denote a finite-dimensional, nonzero vector space over F.

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