grandes-ecoles 2019 Q21

grandes-ecoles · France · centrale-maths2__psi Matrices Diagonalizability and Similarity

We denote $A = \left(\begin{array}{ccc} 1 & 3 & -7 \\ 2 & 6 & -14 \\ 1 & 3 & -7 \end{array}\right)$ and $u$ the endomorphism of $\mathbb{C}^3$ canonically associated with $A$.
Prove that $A$ is similar to the matrix $\operatorname{diag}\left(J_2, J_1\right)$. Give the value of an invertible matrix $P$ such that $A = P \operatorname{diag}\left(J_2, J_1\right) P^{-1}$.

We denote $A = \left(\begin{array}{ccc} 1 & 3 & -7 \\ 2 & 6 & -14 \\ 1 & 3 & -7 \end{array}\right)$ and $u$ the endomorphism of $\mathbb{C}^3$ canonically associated with $A$.

Prove that $A$ is similar to the matrix $\operatorname{diag}\left(J_2, J_1\right)$. Give the value of an invertible matrix $P$ such that $A = P \operatorname{diag}\left(J_2, J_1\right) P^{-1}$.

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