Question: Let v 1 , v 2 ,? ,v n be a basis in a vector space V. Assume also that the first k vectors v
Let v 1 , v 2 ,? ,v n be a basis in a vector space V. Assume also that the first k vectors v 1 , v 2 ..... v k of the basis are eigenvectors of an operator A, corresponding to an eigenvalue ? (i.e. that Av j = ?v j , j = 1,2, ..., k). Show that in this basis the matrix of the operator A has block triangular form
Where I k is k x k identity matrix and B is some (n ? k) x (n ? k) matrix.
XIk ) 0 B
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