Page 72 - Statistics and Data Analysis in Geology

Statistics and Data Analysis in Geology- Chapter 3
or
h2 - 34h + 20 = 0
There are no obvious factors in the quadratic equation, so we must apply the
rule for a general solution:

-b+ J- - (-34) c J-342 - 4 x 1 x 20 - 34 + JiDZ
X= =A= -
2a 2x1 2
hi = 33.4 A2 = 0.6

We can check our work by substituting the eigenvalues back into the determi-
nant to see if it is equal to zero, within the error introduced by round-off

So, the eigenvalues we have found are correct within two decimal places.
Before we leave the computation of eigenvalues of 2 x 2 matrices, we should
consider one additional complication that may arise. Suppose we want the eigen-
values of the matrix

A=[ -6 2 41
3
Expressed as a determinant equal to zero, we have

which expands to

or
h2 - 5h + 30 = 0
The roots of this equation are

But this leads to equations involving the square roots of negative numbers:
5 + m
hl = = 2.5 + 4.9i
2
5 - m
A2 = = 2.5 - 4.9i
2
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