(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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12 CAPÍTULO 1. ¢¡¤£¦¥¨§©¢£ ¥£§§¥ £<br />
AB − BA A 2 <br />
B 2 <br />
¢ ¡ <br />
¡ ¨ § A B C <br />
<br />
(A (B + C)) T = B T A T + C T A T<br />
£¢<br />
(A (B + C)) T = (B + C) T A T = B T + C T A T = B T A T + C T A T<br />
¨¥ ¨ A B C <br />
1 2 3<br />
¡ ¨ § A B <br />
<br />
A + B = 4 5 6<br />
7 8 9<br />
A ¡ ¡ B ¡ <br />
A =<br />
a11 a12 a13<br />
¨ <br />
<br />
<br />
¨¥<br />
<br />
<br />
¢<br />
<br />
A ¨ T A B A T = −A B = B<br />
B 3 × 3<br />
a21 a22 a23<br />
a31 a32 a33<br />
a11 a21 a31<br />
¢ £¢<br />
A T = a12 a22 a32<br />
a13 a23 a33<br />
¡ ¡ £¢<br />
A<br />
A = −AT ⇐⇒<br />
⇐⇒<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
a11 = −a11<br />
a12 = −a21<br />
a13 = −a31<br />
a22 = −a22<br />
a23 = −a32<br />
a33 = −a33<br />
<br />
<br />
a11 a12 a13<br />
a21 a22 a23<br />
a31 a32 a33<br />
⇐⇒<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
<br />
2a11 = 0<br />
a21 = −a21<br />
a31 = −a13<br />
2a22 = 0<br />
a32 = −a23<br />
2a33 = 0<br />
<br />
A ¢ <br />
B<br />
<br />
b11 b12 b13<br />
B =<br />
B T =<br />
b21 b22 b23<br />
b31 b32 b33<br />
b11 b21 b31<br />
b12 b22 b32<br />
b13 b23 b33<br />
<br />
a11<br />
= − a12<br />
a21<br />
a22<br />
a31<br />
a32<br />
a13 a23 a33<br />
⇐⇒<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
<br />
<br />
.<br />
<br />
.<br />
a11 = a22 = a33 = 0<br />
a21 = −a21<br />
a31 = −a13<br />
a32 = −a23,
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