Orthogonal Matrix : Diagonalizability
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Dtermine whether or not the following matrix
A= 5 0 2
0 5 0
2 0 5
is diagonalizable. If it is, then determine
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
Eigenvlaues, determinants and inverses are used to determine the diagonlizability of a given matrix.