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.

Transcribed Image Text:

XIk в) 0 О B XIk в) 0 О B

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V 1 V 2 v n be a basis of V V 1 V 2 v k be eigenvectors such that Av j v j for j 1 2 3k ... View the full answer