436 HW8.pdf - MATH 436 LINEAR ALGEBRA HOMEWORK 8 Solutions Working with eigenvalues and eigenvectors Problem 1 Suppose f L(C and dim range f = k Show

436 HW8.pdf - MATH 436 LINEAR ALGEBRA HOMEWORK 8 Solutions...

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MATH 436 LINEAR ALGEBRA HOMEWORK 8 Solutions Working with eigenvalues and eigenvectors Problem 1.Supposef∈ L(C)anddim rangef=kShow thatfhas atmostk+ 1distinct eigenvalues. Problem 2.SupposeVis a complex vector space andf∈ L(V).Provethatfhas an invariant subspace of dimensionjforj= 1, . . . , Problem 3.LetVbe a finite-dimensional nonzero complex vector space.
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