# 高等代数习题（二）

## 高等代数习题（二）

$$A_0A_i-A_iA_0=A_{i+1},\quad A_0A_m=A_mA_0,\quad A_jA_k=A_kA_j$$

$$[x_0,x_i]=x_{i+1},\quad[x_0,x_m]=0,\quad[x_j,x_k]=0$$

$$A^nB=BA^n+\binom{n}{1}(\text{ad}A)(B)A^{n-1}+\binom{n}{2}(\text{ad}A)^2(B)A^{n-2}+\cdots+(\text{ad}A)^n(B).$$

$$N=\{A\in M_n(\mathbb{C}):AB-BA\in M,\forall B\in M\}.$$

$$\text{tr}(AP)=\sum_{i=1}^n\lambda_if(\lambda_i)=0,$$

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