若已知ab=ba,证明(a+b)的平方等于a的平方加上两倍ab加上b的平方。。。线性代数问题
\u4e00\u4e2a\u7ebf\u6027\u4ee3\u6570\u95ee\u9898\uff1a\u8bc1\u660eAB-BA\u4e0d\u7b49\u4e8eE\u8003\u8651\u77e9\u9635\u7684\u8ff9\u3002
Tr(AB-BA)=Tr(AB)-Tr(BA)
\u53c8\u56e0\u4e3aTr(AB)=Tr(BA)(\u56e0\u4e3aTr(AB)=\u2211aijbji\uff0c
Tr(BA)=\u2211bijaji,\u6240\u4ee5\uff0cTr(AB)=Tr(BA))\uff0c\u6240\u4ee5
Tr(AB-BA)=0
\u7136\u800c
Tr(E)\u22600
\u6240\u4ee5AB-BA\u2260E\u3002
\u8c22\u8c22yjguy\u5171\u540c\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898~~~ ^_^
A²-2AB=E
A\uff08A-2B\uff09=E
\u6240\u4ee5A\u53ef\u9006\u3002\u9006\u77e9\u9635\u4e3a\uff08A-2B\uff09
\u6240\u4ee5\uff08A-2B\uff09A=E
A²-2BA=E
\u53c8\u56e0\u4e3aA²-2AB=E
\u6240\u4ee5AB=BA
\u6240\u4ee5AB-BA+A=A\u53ef\u9006
=a^2+2ab+b^2
绛旓細鍥犱负 AB=BA 鎵浠 (AB)^T=B^TA^T=BA=AB 鎵浠 AB 鏄绉扮煩闃.鐢A,B姝ｅ畾, 瀛樺湪鍙嗙煩闃礟,Q浣 A=P^TP,B=Q^TQ.鏁 AB = P^TPQ^TQ 鑰 QABQ^-1=QP^TPQ^T = (PQ)^T(PQ) 姝ｅ畾, 涓斾笌AB鐩镐技 鏁 AB 姝ｅ畾.
绛旓細(a+b)(a+b)=axa+axb+bxa+bxb =a^2+2ab+b^2
绛旓細杩欎釜棰樼洰鍐呭灞炰簬鐭╅樀涔樻硶鐨勮繍绠楄寰嬨傛垜浠彲浠ユ妸鍏朵腑绗竴涓狝+B鐭╅樀鐪嬫垚涓涓柊鐨勭煩闃礐锛岄偅涔 (A+B)*(A+B)=C*(A+B)=C*A+C*B=(A+B)*A+(A+B)*B=A*A+B*A+A*B+B*B 锛1锛夊洜涓洪鐩宸茬煡 A*B=B*A 鎵浠ワ紙1锛夊紡宸﹁竟=A*A+2*A*B+B*B 璇佹瘯銆
绛旓細1.宸﹁竟=A(B+C)=AB+AC =BA+CA =(B+C)A =鍙宠竟 2.宸﹁竟=A(BC)=(AB)C =(BA)C =BAC =B(AC)=B(CA)=BCA =(BC)A =鍙宠竟
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