matlab 与 stata 在计算特征向量方面存在差别——同一矩阵,采用matlab 与 stata 计算得到的特征根是相同的,但在计算特征向量方面却存在差别。具体而言,有些特征向量是相同的,而一部分却是绝对值相同,而符号刚好相反(互为相反数)。哪一个结果才是可靠的哩?期待高手指点,谢谢!
下面以具体数据例子加以说明(可直接拷贝检验之):
1.原始数据(矩阵):
| 852.6777  | 804.5046  | 857.0354  | 827.1819  | 854.9609  | 841.2367  | 751.9389  | 
| 804.5046  | 844.1070  | 776.3881  | 784.0371  | 799.1031  | 844.2438  | 747.2521  | 
| 857.0354  | 776.3881  | 948.4691  | 854.2202  | 891.5663  | 866.4708  | 770.1967  | 
| 827.1819  | 784.0371  | 854.2202  | 843.7187  | 832.8228  | 860.2821  | 749.9695  | 
| 854.9609  | 799.1031  | 891.5663  | 832.8228  | 898.5519  | 858.7185  | 760.4418  | 
| 841.2367  | 844.2438  | 866.4708  | 860.2821  | 858.7185  | 948.7695  | 792.4689  | 
| 751.9389  | 747.2521  | 770.1967  | 749.9695  | 760.4418  | 792.4689  | 704.7535  | 
2. stata运算得到的特征根和特征向量:
(1)特征根:
| 5765.472 | 141.138 | 64.760 | 30.435 | 24.288 | 8.946 | 6.008 | 
(2)特征向量(与特征根顺序对应):
| 0.380 | -0.085 | 0.415 | 0.347 | -0.245 | -0.430 | 0.558 | 
| 0.367 | 0.610 | 0.416 | -0.082 | 0.278 | -0.196 | -0.445 | 
| 0.392 | -0.618 | -0.156 | -0.097 | 0.559 | -0.300 | -0.169 | 
| 0.377 | -0.062 | -0.244 | 0.692 | -0.257 | 0.279 | -0.414 | 
| 0.387 | -0.306 | 0.314 | -0.537 | -0.478 | 0.342 | -0.157 | 
| 0.394 | 0.335 | -0.687 | -0.310 | -0.249 | -0.275 | 0.165 | 
| 0.346 | 0.174 | -0.023 | 0.014 | 0.439 | 0.646 | 0.489 | 
3.matlab去处得到的特征根和特征向量
(1)特征根:
| 5765.472  | 141.138  | 64.760  | 30.435  | 24.288  | 8.946  | 6.008  | 
(2)特征向量(与特征根顺序对应:
| 0.380  | 0.085  | 0.415  | 0.347  | -0.245  | 0.430  | 0.558  | 
| 0.367  | -0.610  | 0.416  | -0.082  | 0.278  | 0.196  | -0.445  | 
| 0.392  | 0.618  | -0.156  | -0.097  | 0.559  | 0.300  | -0.169  | 
| 0.377  | 0.062  | -0.244  | 0.692  | -0.257  | -0.279  | -0.414  | 
| 0.387  | 0.306  | 0.314  | -0.537  | -0.478  | -0.342  | -0.157  | 
| 0.394  | -0.335  | -0.687  | -0.310  | -0.249  | 0.275  | 0.165  | 
| 0.346  | -0.174  | -0.023  | 0.014  | 0.439  | -0.646  | 0.489  | 
结论:实例中,特征根相同;但特征向量中第2个与第6个,互为相反数。哪个才是“对”的?!期待指点!