# What is the limit of exp(-kM/T)?

1. Jul 12, 2005

### CarlB

What is the limit of exp(-kM/T)???

Let M be a matrix:

$$\left(\begin{array}{cc}a & b \\c & d\end{array}\right)$$

where a,b,c and d are complex constants. Let k and T be positive real numbers. Is there a closed formula for this limit?

$$\begin{array}{c}\lim \\ T->0^{+}\end{array} \;\;\; e^{-kM/T}$$

Of course the answer will not depend on k, or T.

Carl

Hint:
http://mathworld.wolfram.com/JordanMatrixDecomposition.html

Last edited: Jul 12, 2005
2. Jul 12, 2005

### Jelfish

Is this what you meant?

$$\lim\limit_{T\to 0^+}e^{-kM/T}$$