In this part, $a$ denotes an endomorphism of $\mathbf { C } ^ { n }$. We use the decomposition $\mathbf { C } ^ { n } = \bigoplus _ { i = 1 } ^ { r } E _ { i }$ where $E _ { i } = \operatorname { Ker } \left( a - \lambda _ { i } id _ { \mathbf { C } ^ { n } } \right) ^ { m _ { i } }$, with the projections $p_i$ and inclusions $q_i$ as defined. Let $( i , j ) \in \llbracket 1 ; r \rrbracket ^ { 2 }$. Express $p _ { i } q _ { j }$ and then $\sum _ { i = 1 } ^ { r } q _ { i } p _ { i }$ in terms of the endomorphisms $id _ { \mathbf { C } ^ { n } }$ and $id _ { E _ { j } }$.
In this part, $a$ denotes an endomorphism of $\mathbf { C } ^ { n }$. We use the decomposition $\mathbf { C } ^ { n } = \bigoplus _ { i = 1 } ^ { r } E _ { i }$ where $E _ { i } = \operatorname { Ker } \left( a - \lambda _ { i } id _ { \mathbf { C } ^ { n } } \right) ^ { m _ { i } }$, with the projections $p_i$ and inclusions $q_i$ as defined.
Let $( i , j ) \in \llbracket 1 ; r \rrbracket ^ { 2 }$. Express $p _ { i } q _ { j }$ and then $\sum _ { i = 1 } ^ { r } q _ { i } p _ { i }$ in terms of the endomorphisms $id _ { \mathbf { C } ^ { n } }$ and $id _ { E _ { j } }$.