[理工] [線代]-一題簡單的對角化

[GI9 ( )]

Let V be the vector space of all nxn matrices over R.

For a given matrix A屬於V , define a linear transformation T_A:V→V by

T_A(B)=AB-BA


For general n , consider the family

Γ＝{T_A：A屬於V ,A is a diagonal matrix} of linear transformation

Prove that Γ is simultaneously diagonalizable


這題配分5分....

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