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CHAPTER
Complex Vector Spaces
I N T R O D U C T I O N : Up to now we have considered only vector spaces for which the scalars are real numbers. However,
for many important applications of vectors, it is desirable to allow the scalars to be complex numbers. For example, in
problems involving systems of differential equations, complex eigenvalues are often the case of greatest interest.
In the first three sections of this chapter we will review some of the basic properties of complex numbers, and in subsequent
sections we will discuss vector spaces in which scalars can be complex numbers.
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