grandes-ecoles 2010 QIID2

grandes-ecoles · France · centrale-maths2__pc Matrices Diagonalizability and Similarity

We assume in this question that $\mathbb { K }$ is equal to $\mathbb { C }$.
Does the result that two non-zero matrices of $\mathcal { M } _ { 0 } ( 2 , \mathbb { C } )$ are similar if and only if they have the same characteristic polynomial remain true for two non-zero matrices of $\mathcal { M } _ { 0 } ( n , \mathbb { C } )$, with $n \geq 3$?

We assume in this question that $\mathbb { K }$ is equal to $\mathbb { C }$.

Does the result that two non-zero matrices of $\mathcal { M } _ { 0 } ( 2 , \mathbb { C } )$ are similar if and only if they have the same characteristic polynomial remain true for two non-zero matrices of $\mathcal { M } _ { 0 } ( n , \mathbb { C } )$, with $n \geq 3$?

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