# Why expm(2*A) != expm(A) @ expm(A)

According to Matrix exponential, if `XY = YX`

, then `exp(X)exp(Y) = exp(X+Y)`

. However when I run the following in Python:

```
import numpy as np
from scipy.linalg import expm
A = np.arange(1,17).reshape(4,4)
print(expm(2*A))
[[ 306.63168024 344.81465009 380.01335176 432.47730444]
[ 172.59336774 195.36562731 214.19453937 243.76985501]
[ -35.40485583 -39.87705598 -42.94545895 -50.01324379]
[-168.44316833 -190.32607875 -209.76427134 -237.72069322]]
print(expm(A) @ expm(A))
[[1.87271814e+30 2.12068332e+30 2.36864850e+30 2.61661368e+30]
[4.32685652e+30 4.89977229e+30 5.47268806e+30 6.04560383e+30]
[6.78099490e+30 7.67886126e+30 8.57672762e+30 9.47459398e+30]
[9.23513328e+30 1.04579502e+31 1.16807672e+31 1.29035841e+31]]
```

I get two very different results. Note that `@`

is just the dot product.

I also tried it in Matlab and the two results are the same as expected. What am I missing here?

sophros
answered question

### 1 Answer

To me the root cause of this issue should be similar to the one described in the following NumPy bug report.

sophros
posted this

## Have an answer?

JD

Maybe this is related to the rounding errors?