3. (a) Suppose N : V → V and N' : V → V are nilpotent of index r and s respectively and NN' = N'N. Use the binomial theorem to show that N + N' is nilpotent. (b) Show that a linear map which is both...

3. (a) Suppose N : V → V and N' : V → V are nilpotent of index r<br>and s respectively and NN' = N'N. Use the binomial theorem to<br>show that N + N' is nilpotent.<br>(b) Show that a linear map which is both diagonalisable and nilpotent<br>must be the zero linear map.<br>

Extracted text: 3. (a) Suppose N : V → V and N' : V → V are nilpotent of index r and s respectively and NN' = N'N. Use the binomial theorem to show that N + N' is nilpotent. (b) Show that a linear map which is both diagonalisable and nilpotent must be the zero linear map.

Jun 04, 2022

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3. (a) Suppose N : V → V and N' : V → V are nilpotent of index r and s respectively and NN' = N'N. Use the binomial theorem to show that N + N' is nilpotent. (b) Show that a linear map which is both...

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