Since we introduced terminology in this
unit, let's introduce some more.  Now, we're
going to find out that there is a finite
number of eigenvalues. And we're going to
denote that set as lambda_0, lambda_1, and so forth.  And that set altogether
we're going to denote with the capital
lambda of A.  And that is the set of
all eigenvalues corresponding to matrix
A. Okay.  And that's known as the spectrum of
matrix A.  The spectral radius of matrix A
is defined as the largest absolute value
of any of the eigenvalues of matrix A. Okay?
So why do we call this the spectral
radius.  Well, you can think of all of the
eigenvalues, they're scalars, and therefore
they are complex valued numbers, well
real or complex values.  And if you put
them all in the complex plane, and you
know which of the eigenvalues has
largest magnitude, then you know that
this circle --that's not much of a circle --
this circle with radius the spectral
radius of A includes all of the
eigenvalues of matrix A -- spectral radius.
