What Is the Difference Between a Transition Matrix and a Jacobian?

[HMT]

Hi:

I`m new here, can someone tell me which is the difference between the transition matrix and the Jacobian?, I did some exercises of the both topics, but How is it related?

Thanks for the attention

Sorry for my English writing, but English is not my native language.

 

[Alesak]

Hi,

by transition matrix, do you mean change-of-basis matrix?

Jacobian gives linear approximation of a smooth function between two euclidean spaces at given point.

 

[HMT]

Yes the transition matrix & change of basis matrix means the same, but for example in the change of coordinates, we need to get the Jacobian of the transformation (for the metric tensor etc), but I`m now feel confused between the matrix of the linear transformation, and the Jacobian of a transformation.

 

[lavinia]

Yes the transition matrix & change of basis matrix means the same, but for example in the change of coordinates, we need to get the Jacobian of the transformation (for the metric tensor etc), but I`m now feel confused between the matrix of the linear transformation, and the Jacobian of a transformation.

In a change of coordinates, the Jacobian gives a change of basis at each point of the domain. The basis change change varies from point to point.