TABLE OF CONTENTS Leverrier's method for the generation of the characteristic polynomial also follows a prescribed procedure. The n coefficients of the polynomial
are calculated by following a rather simple procedure. The computation begins by setting A 1= A, obtaining the trace of A, and then finding a coefficient
Two new matrices are then formed:
and
The procedure is then repeated n times using the recurrence relationships
and
Again with
obtain tr A = ?9 and let ? 1= ?tr A = 9. Then, with A 1 = A
and
Next
and
The final step is the determination of ? 3
These values of ? are the coefficients of p( ?)
Leverrier's method also provides the inverse of A. This bonus comes from a simple computation involving B n ?1 and ? n
With B 2 and ? 3 taken from Example 7.4:
This can be verified
