符号矩阵的特征值
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我想8×8象征性的符号特征值矩阵。但是在我使用了eig()函数,Matlab跑一段时间,返回一个非常非常长的表达式开始“RootOf{…”我相信意味着没有解决方案。这是代码。
信谊t1 t2 t11 t22 t3 t33 t4 t44;
信谊H;
信谊kx肯塔基州;
= 1.05 * 180(π/;
v = 0.3;
w = 0.11;
d =π/ 4 * (3 * 2.46);
H = (t1 - v / 2 w w w * exp(我* 2 *π/ 3)w w * exp(我* 2 *π/ 3)w; t11 - v / 2 w w w * exp(我* 2 *π/ 3)w * exp(我* 2 *π/ 3)w * exp(我* 2 *π/ 3)w * exp(我* 2 *π/ 3);w w v / 2 t2 0 0 0 0; w w t22 v / 2 0 0 0 0;w * exp(我* 2 *π/ 3)w 0 0 v / 2 t3 0 0;w * exp(我* 2 *π/ 3)w * exp(我* 2 *π/ 3)0 0 t33 v / 2 0 0;w * exp(我* 2 *π/ 3)w 0 0 0 0 v / 2 t4;w * exp(我* 2 *π/ 3)w * exp(我* 2 *π/ 3)0 0 0 0 t44 v / 2];
dd = eig (H);
谁能给我一个提示符号矩阵的特征值的计算方法,“H”?要多长时间?我的终极目标是情节的8个特征值的范围kx =[1:0.1:1]和肯塔基州= [1:0.1:]。非常感谢。
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沃尔特·罗伯森
2012年3月6日
RootOf()可能是一个有效的解决方案的一部分。MuPAD有时表达甚至根RootOf ()
枫花了大约1秒才找到特征值的公式。特征值是一个八阶多项式的根在你的t *变量。
内部注意:枫格式,矩阵
eval (”<、>”(”< | >”(- (1/2)* v, t1, w w w * exp(2 *我*π* (1/3)),w w * exp(2 *我*π* (1/3)),w),”< | >”(t11 - (1/2) * v, w w w * exp(2 *我*π* (1/3)),w * exp(2 *我*π* (1/3)),w * exp(2 *我*π* (1/3)),w * exp(2 *我*π* (1/3))),”< | >”(w w (1/2) * v, t2, 0, 0, 0, 0),”< | >”(w w t22 (1/2) * v, 0, 0, 0, 0),”< | >”(w * exp(2 *我*π* (1/3)),w, 0, 0, (1/2) * v, t3, 0, 0),”< | >”(w * exp(2 *我*π* (1/3)),w * exp(2 *我*π* (1/3)),0,0,t33, (1/2) * v, 0, 0),”< | >”(w * exp(2 *我*π* (1/3)),w, 0, 0, 0, 0, (1/2) * v, t4),”< | >”(w * exp(2 *我*π* (1/3)),w * exp(2 *我*π* (1/3)),0,0,0,0,t44, (1/2) * v)),(π=π,我= =(1/180)*(105/100)*π,v = 3/10, w = 11/100, d =π/ 4 * (3 * 246/100)))
= = = = = =
用你的全部方程按电子邮件:
在这里工作,因为它是不可能的格式的评论:
枫:
var:= =(1/180)*(105 *(1/100))*π,v = 3/10, w = 11/100, d =π/ 4 * (3 * (246 * (1/100))),t1 = 3 * (d * cos ((1/2) *) + kx-I * (d * sin((1/2) *) +肯塔基州)),t11 = 3 * (d * cos ((1/2) *) + kx + I * (d * sin((1/2) *) +肯塔基州)),t2 = 3 * (d * cos ((1/2) *) + kx-I * (d * sin(-(1/2) *) +肯塔基州)),t22 = 3 * (d * cos ((1/2) *) + kx + I * (d * sin(-(1/2) *) +肯塔基州)),t3 = 3 * (d * cos(2 *π* (1/3)- (1/2)*)+ kx-I * (d * sin(2 *π*(1/3)-(1/2)*)+肯塔基州)),t33 = 3 * (d * cos(2 *π* (1/3)- (1/2)*)+ kx + I * (d * sin(2 *π*(1/3)-(1/2)*)+肯塔基州)),t4 = 3 * (d * cos(4 *π* (1/3)- (1/2)*)+ kx-I * (d *罪(4 *π*(1/3)-(1/2)*)+肯塔基州)),t44 = 3 * (d * cos(4 *π* (1/3)- (1/2)*)+ kx + I * (d *罪(4 *π*(1/3)-(1/2)*)+肯塔基州)),3 = w * exp (- (1/3) * (* 2) * Pi));H:= <、>”(”< | >”(- (1/2)* v, t1, w w, 3, w, 3, w),”< | >”(t11 - (1/2) * v, w w, 3, 3, 3, 3),”< | >”(w w (1/2) * v, t2, 0, 0, 0, 0),”< | >”(w w t22 (1/2) * v, 0, 0, 0, 0),”< | >”(3 w, 0, 0, (1/2) * v, t3, 0, 0),”< | >”(3、3 0 0 t33 (1/2) * v, 0, 0),”< | >”(3 w, 0, 0, 0, 0, (1/2) * v, t4),”< | >”(3 3 0,0,0,0,t44, (1/2) * v));
HH:= eval (eval (H, var), var);
dd:= LinearAlgebra(特征值)(HH);
我在等待结果。