  # Jordan cannonical form worked example

### Real triple root example with dimension 3 and eigenspace spanned by the eigenvalue with dimension 2.

Let's make another worked example of Jordan form calculation for a 3x3 matrix, now with a only eigenvalue with triple and eigenspace spanned with 2 dimension.

Let's the matrix The fist we calculate the roots of characteristic polynomial: therefore we have λ=3 triple (algebraic) multiplicity eigenvalue.

Calculate the dimension of eigenspace corresponding to this eigenvalue, ie, calculate

dim[Ker(A-3I)]

for this, we make

(A-3I)X=0

and have the linear equations system So, we have two eigenvectors so, 2 is the dimension of eigenespace, therefore A is not diagonalizable and Jordan cannonical form is Calculate the eigenvector basis, using the method 1 seen in the theory (see theory in section "Cannonical Jordan form") ,ie, calculate v3 such us

(A-3I)v3 = k1 v1 + k2 v2

them, we have the system we have now the eigenvectors basis

we are done because

A = PJP-1

where and P is the change of basis matrix, formed by eigenvectors placed as column vectors, ie ## Was useful? want add anything?

### Necip:

2020-11-26 19:20:30
Thanks for example. By the way, my calculator shows Jordan matrix as a ((3 1 0)(0 3 0)(0 0 3) with a little difference from your solution. Are both of these answer correct?

### Carlos:

2021-01-17 18:10
Hi Necip.

Absolutly, both anwers are correct. Only you must take care with the change of basis matrix.

Regards
Carlos

### Josh:

2021-12-01 04:00:37
I agree with Necip, but this is a great example!

### Carlos:

2021-12-02 02:15:37
Thanks a lot Josh.

Really he is correct, both answers are true, you only have to change the changing basis matrix formed by the eigenvectors, it must be reordered too.

Regards
Carlos 快乐飞艇开奖 快乐飞艇做任务靠谱吗 熊猫乐园快乐飞艇 华创投资快乐飞艇靠谱吗 快乐飞艇综合走势图 快乐飞艇app首页 快乐飞艇官网 快乐飞艇是不是官方的 快乐飞艇计划 快乐飞艇彩票 快乐飞艇34567玩法 快乐飞艇app下载