Share
Explore BrainMass

Orthogonal Matrix : Diagonalizability

Dtermine whether or not the following matrix
A= 5 0 2
0 5 0
2 0 5
is diagonalizable. If it is, then determine
P'-1(P inverse)AP.

Solution Preview

If a matrix is diagonalizable, then the matrix will have n ( or in this case 3) independent eigenvalues:

Set up the equation: det(A-rI) = 0 to get the characteristic equations:

| 5-r 0 2 |
| 0 5-r 0 | = 0
| 2 0 5-r|

(5-r)^3 - 4(5-r) = 0
(5-r)[(5-r)^2 - 4] = 0

Thus ...

Solution Summary

Eigenvlaues, determinants and inverses are used to determine the diagonlizability of a given matrix.

$2.19