Finding unitary transformation

[seek]

Homework Statement

Find a unitary transformation that diagonalizes the matrix:

1 1 1 -3
1 1 1 -3
1 1 1 -3
-3 -3 -3 -9

Homework Equations

The Attempt at a Solution

So before I even start with finding the eigenvalues for this, I know there has to be a way to reduce this so I don't have to find the determinant of a 4x4 matrix. Clearly none of these rows are independent. We haven't gone over this very thoroughly in class, so I'm not too sure about the best way to go about this.

 

[Dick]

There's no real shortcut here. Sometimes you can find eigenvectors by inspection and guessing. Two of them are pretty easy to find. I'm not how you would guess the other two, unless you are better at guessing than I am. Just evaluate the determinant.