设U∈Cm×m与V∈Cn×n均是酉矩阵 证明：(UAVH)+=VA+UH．请帮忙给出正确答案和分析

正确答案：利用UV为酉矩阵和A⁺的运算性质容易验证UAV^H和VA⁺U^H满足M－P广义逆定义的四个方程：(1)UAV^HVA⁺U^HUAV^H=UAA⁺AV^H=UAV^H：(2)VA⁺U^HUAV^HVA⁺U^H=VA⁺AA⁺U^H=VA⁺U^H：(3)(UAV^HVA⁺U^H)^H=(UAA⁺U^H)^H=U(AA⁺)^HU^H=UAA⁺U^H=UAV^HVA⁺U^H：(4)类似(3)可得(VA⁺U^HUAV^H)^H=VA⁺U^HUAV^H．所以(UAV^H)⁺=VA⁺U^H．
利用U,V为酉矩阵和A+的运算性质,容易验证UAVH和VA+UH满足M－P广义逆定义的四个方程：(1)UAVHVA+UHUAVH=UAA+AVH=UAVH：(2)VA+UHUAVHVA+UH=VA+AA+UH=VA+UH：(3)(UAVHVA+UH)H=(UAA+UH)H=U(AA+)HUH=UAA+UH=UAVHVA+UH：(4)类似(3)可得(VA+UHUAVH)H=VA+UHUAVH．所以(UAVH)+=VA+UH．