Question: OO ... 0 0 0 0 ... H X OO ... 0 O ... KO O o ... . . . O O oo ...

OO ... 0 0 0 0 ... H X OO ... 0 O ... KO O o ... . . . O O oo ... OOH O O oo ... LOOK O For each of the eigenvalues ( of A, determine the smallest m E Zo for which oo ... 0. O We suppose the lower right block is a k x k-matrix and the upper left block, therefore, . . . OO For each of the eigenvalues of A, determine its generalised eigenspace. Exercise 3.2.10: Let A E IF ER, Cy and consider the linear map A E L( IF"; IF" ) deter- For each of the eigenvalues of A, determine its algebraic multiplicity. For each of the eigenvalues of A, determine its geometric multiplicity. .. .Koo0 For each of the eigenvalues of A, determine its eigenspace. O ...OOO O O ...0 0 = What are the eigenvalues of A? W((, A) = ker((A - (In)m). Answer the following questions. mined by the n x n-matrix is a (n - k) x (n - k)-matrix. a)

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