# Thread: Orthogonally diagonalize the symmetric matrix

1. ## Orthogonally diagonalize the symmetric matrix

Im really lost on how to do these, i got no idea, can someone explain what i need to do to solve this, thanks

Orthogonally diagonalize the symmetric matrix:

0 1 0
1 0 0
0 0 3

2. I have no idea what the definition of "orthogonal diagonalise" is. To diagonalise this matrix $S$, you need to swap the role of the first and second column and keep third fixed, so use $P$
0 1 0
1 0 0
0 0 1
and you will see that $PSP^{-1}$ is a diagonal matrix. In case "orthogonal diagonalise" means $PP^t=I$, then this $P$ should work.