- #1
Felafel
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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?