问答题
3阶矩阵A与对角阵
【正确答案】
【答案解析】存在可逆阵P，使P
-1
AP=D，故A=PDP
-1
，
B=(PDP
-1
-λ
1
PP
-1
)(PDP
-1
-λ
2
PP
-1
)(PDP
-1
-λ
3
PP
-1
)=P(D-λ
1
E)P
-1
P(D-λ
2
E)P
-1
P(D-λ
3
E)P
-1
=P(D-λ
1
E)(D-λ
2
E)(D-λ
3
E)P
-1
=
B=(PDP
-1
-λ
1
PP
-1
)(PDP
-1
-λ
2
PP
-1
)(PDP
-1
-λ
3
PP
-1
)=P(D-λ
1
E)P
-1
P(D-λ
2
E)P
-1
P(D-λ
3
E)P
-1
=P(D-λ
1
E)(D-λ
2
E)(D-λ
3
E)P
-1
=