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Mathematica的bug?

Mathematica的bug?# Computation - 科学计算

b*h2004-05-28 07:05

1 楼

Why the eigenvector of a matrix can be 0. (Please look at the last row of Out[2]).
In[1]:=
mat={{0,1/3,2/3,0,0},{0,0,0,1/4,3/4},{0,0,0,1/2,1/2},{1,0,0,0,0},{1,0,0,0,0}};
In[2]:=
Eigenvectors[mat]
Out[2]//OutputForm=
-1 + I Sqrt[3] 1 - I Sqrt[3] 1 - I Sqrt[3]
{{--------------, -1 + -------------, -1 + -------------, 1, 1},
2 2 2
-1 - I Sqrt[3] 1 + I Sqrt[3] 1 + I Sqrt[3]
{--------------, -1 + -------------, -1 + ---------

y*t2004-05-28 07:05

2 楼

The matrix has a Jordan block of size 2X2. So it only has 4 eigenvectors.
Nothing wrong here.

【在 b******h 的大作中提到】

: Why the eigenvector of a matrix can be 0. (Please look at the last row of Out[2]).
: In[1]:=
: mat={{0,1/3,2/3,0,0},{0,0,0,1/4,3/4},{0,0,0,1/2,1/2},{1,0,0,0,0},{1,0,0,0,0}};
: In[2]:=
: Eigenvectors[mat]
: Out[2]//OutputForm=
: -1 + I Sqrt[3] 1 - I Sqrt[3] 1 - I Sqrt[3]
: {{--------------, -1 + -------------, -1 + -------------, 1, 1},
: 2 2 2
: -1 - I Sqrt[3] 1 + I Sqrt[3] 1 + I Sqrt[3]

b*h2004-05-28 07:05

3 楼

问题是在Mathematica里如何才能对角化mat呢？

【在 y**t 的大作中提到】

: The matrix has a Jordan block of size 2X2. So it only has 4 eigenvectors.
: Nothing wrong here.