- #1

Brewer

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## Homework Statement

Given the matrix A =

(1 1 -1)

(1 -1 1)

(-1 1 1)

write down the unitary matrix U which diagonalises A. Verify that [tex]U^\dagger AU[/tex] is diagonal with the eigenvalues of A along the diagonal.

## Homework Equations

## The Attempt at a Solution

The eigenvalues were calculated earlier in the question, and found to be -2, 1 and 2. I know these are correct.

For U I would have said that the question (phrased as it is with "write down" so should not require any thinking) wants me to say that U has the same diagonal as A, but zeros in the other 6 elements of the matrix. And because this is a real matrix the adjoint of the matrix will be itself, because it is its own transpose. However when I come to calculate the final part of the question, I don't get a diagonal matrix, or the eigenvalues appearing anywhere, so I'm a little confused. Any pointers in the right direction wuold be appreciated.