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Let A be a matrix with an eigenvalue λ that has an algebraic multiplicity of k,...

Let A be a matrix with an eigenvalue λ that has an algebraic multiplicity of k, but a geometric multiplicity of p < k, i.e. there are p linearly independent generalised eigenvectors of rank 1 associated with the eigenvalue λ, equivalently, the eigenspace of λ has a dimension of p. Show that the generalised eigenspace of rank 2 has at most dimension 2p.

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