# Transition matrix, Jacobian.

1. Mar 16, 2012

### HMT

Hi:

Im 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.

2. Mar 17, 2012

### 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.

3. Mar 17, 2012

### 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 Im now feel confused between the matrix of the linear transformation, and the Jacobian of a transformation.

4. Mar 17, 2012

### lavinia

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.