AT = (B-C)T = BT-CT = B+C
AAT = (B-C)(B+C) = B²+BC-CB-C²
ATA = (B+C)(B-C) = B²-BC+CB-C²
1)若 AAT=ATA
那么 B²+BC-CB-C² = B²-BC+CB-C²
即 2BC = 2CB , 即 BC = CB
2)若 BC=CB
那么 AAT = B²+BC-CB-C² = B²+CB-BC-C² = ATA
即 AAT = ATA
由1)2)得: AAT=ATA充要条件BC=CB
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