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## Homework Statement

##\phi## is an endomorphism in ##\mathbb{E}^3## associated to the matrix

(1 0 0)

(0 2 0) =##M_{\phi}^{B,B}##=

(0 0 3)

where B is the basis: B=((1,1,0),(1,-1,0),(0,0,-1))

Find an orthonormal basis "C" in ##\mathbb{E}^3## formed by eigenvectors of ##\phi##

## The Attempt at a Solution

Being the eigenvalues the elements of the diagonal 1, 2, 3

Aren't (1, 0, 0), (0,2,0), (0,0,3) three orthonormal vectors already?

Or should I write the endomorphism according to the canonical basis first and find new values?