假設A的eiganvalues 為 -2, a, b
2 4 -6 r13 r23 2 4 -6 r12(-2) 2 4 -6
4 2 -6 --> 4 2 -6 --> 0 -6 6
-6 -6 -15 0 0 -27 0 0 -27
det(A) = 2*(-6)*(-27) = 324 = (-2)*a*b
trace(A) = 2+2+(-15) = -11 = (-2)+a+b
a+b = -9
ab = -162
不失一般性假設 a > b
(a+b)^2 = 81 = a^2 + 2ab + b^2 = a^2 + b^2 - 324
a^2 + b^2 = 405
a^2 + b^2 - 2ab = 729 = (27)^2 = (a-b)^2
a+b=-9 a = 9
=> b = -18
a-b=27
A的eiganvalues 為 -2, 9, -18
用計算機驗證一下
http://ppt.cc/PTXI
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 1.160.34.220