A brief summary: Given a linear operator on finite-dimensional vector space .

- For any ordered bases and ,
is similar to .

- is an eigenvalue of is an eigenvalue of (any) matrix representation of w.r.t an ordered basis.
Their eigenvectors are related via the coordinate isomorphism. (See p.458 in Lect21.pdf)

- If has a -invariant subspace, then we are able to find a matrix representation in nice block form. (See p.455.)

After Class Exercises: Ex 9.3 Qn 2(b), 3, 5 (See L21-ace.pdf)

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