grandes-ecoles 2010 QIIG2

grandes-ecoles · France · centrale-maths2__pc Matrices Matrix Algebra and Product Properties

Let $P$ be a matrix of $GL ( 2 , \mathbb { K } )$. Verify that $( P X _ { 0 } P ^ { - 1 } , P H _ { 0 } P ^ { - 1 } , P Y _ { 0 } P ^ { - 1 } )$ is an admissible triple.
Recall that a triple $(X, H, Y)$ of three non-zero matrices of $\mathcal{M}(n, \mathbb{K})$ is an admissible triple if $[H,X]=2X$, $[X,Y]=H$, $[H,Y]=-2Y$.

Let $P$ be a matrix of $GL ( 2 , \mathbb { K } )$. Verify that $( P X _ { 0 } P ^ { - 1 } , P H _ { 0 } P ^ { - 1 } , P Y _ { 0 } P ^ { - 1 } )$ is an admissible triple.

Recall that a triple $(X, H, Y)$ of three non-zero matrices of $\mathcal{M}(n, \mathbb{K})$ is an admissible triple if $[H,X]=2X$, $[X,Y]=H$, $[H,Y]=-2Y$.

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