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Unformatted text preview: 1 = n X i =1 1 sλ i e i v T i where ( e i ,v i ,λ i ) are the right and left eigenvectors and corresponding eigenvalues of A . Exercise 4. Let A = ± 1 0 2 3 ² . Find an expression for A n . 1 4 Ainvariant subspaces 2 4 Ainvariant subspaces Consider the linear map A : V → V . A subspace M ⊂ V is said to be Ainvariant if, A ( x ) ∈ M for all x ∈ M . Exercise 5. Show that the following subspaces of V are Ainvariant: (a) N ( A ) (b) R ( A ) (c) N ( AλI ) , where λ ∈ σ ( A ) Exercise 6. Let x ∈ R n . Show that the vector space Ω := span { x,Ax,A 2 x,. ..,A n1 x } is Ainvariant....
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This note was uploaded on 12/09/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at University of California, Berkeley.
 Fall '10
 ClaireTomlin

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