course | course_year | question_number | tags | title | year | |||
---|---|---|---|---|---|---|---|---|
Linear Algebra |
IB |
36 |
|
Paper 4, Section I, |
2021 |
Let
Given $A \in \operatorname{Mat}{n}(\mathbb{C})$, define the linear $\operatorname{map}{A}: \operatorname{Mat}{n}(\mathbb{C}) \rightarrow \operatorname{Mat}{n}(\mathbb{C})$,
(i) Compute a basis of eigenvectors, and their associated eigenvalues, when
What is the rank of
(ii) Now let $A=\left(\begin{array}{ll}0 & 1 \ 0 & 0\end{array}\right)$. Write down the matrix of the linear transformation
What is its Jordan normal form?