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## Homework Statement

Is there a basis of R4 consisting of eigenvectors for A matrix?

If so, is the matrix A diagonalisable? Diagonalise A, if this is possible. If A is not diagonalisable because some eigenvalues are complex, then find a 'block' diagonalisation

of A, involving a 2 × 2 block corresponding to a pair of complex-conjugate eigenvalues.

A=

0 1 0 0

0 0 1 0

0 0 0 1

1 0 0 0

## Homework Equations

## The Attempt at a Solution

I worked out the eigenvalues 1,-1,i,-i. I also worked out real eigenvectors: (-1,1,-1,1)^T and (1,1,1,1)^T. Whenever I try to work out complex eigenvectors I get no free variables..? How come A is "not diagonalisable because some eigenvalues are complex?" What does it mean by find block disgonalisation?