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Summary: CHAPTER 7
Eigenvalues
and
Eigenvectors
7.1 ELEMENTARY PROPERTIES OF EIGENSYSTEMS
Up to this point, almost everything was either motivated by or evolved from the
consideration of systems of linear algebraic equations. But we have come to a
turning point, and from now on the emphasis will be different. Rather than being
concerned with systems of algebraic equations, many topics will be motivated
or driven by applications involving systems of linear differential equations and
their discrete counterparts, difference equations.
For example, consider the problem of solving the system of two first-order
linear differential equations, du1/dt = 7u1 - 4u2 and du2/dt = 5u1 - 2u2. In
matrix notation, this system is
u
1
u
2
=
7 -4
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