# Matrix Transformation

1. Aug 8, 2010

### aliya

Suppose two matrices A and B . i want to transform matrix addition to matrix multiplication. e.g A+B into A.B.
Can anybody please tell me of any way i can do it ,except exponentiation? exponentiation gives an infinite answer.

2. Aug 8, 2010

### HallsofIvy

It is certainly true that $e^{A+ B}= e^Ae^B$ but what do you mean by "exponentiation gives an infinite answer"?

3. Aug 8, 2010

### trambolin

$e^{A+ B}= e^Ae^B$ if and only if $AB = BA$

4. Aug 8, 2010

Don't A and B also need to be n x n matices?

Last edited: Aug 8, 2010
5. Aug 9, 2010

### aliya

"By exponentiation gives an infinite answer" i meant that suppose two matrices A and B, their multiplication A.B gives a finite answer i.e another finite matrix. but e^A.e^B give an infinite answer. doesn't it? Also can you please tell if there exists any X such that A.B=X(e^A.e^B)?

6. Aug 9, 2010

### HallsofIvy

No, it doesn't. If A and B are n by n matrices, then so are $e^A$, $e^B$, and $e^Ae^B$.

7. Aug 9, 2010

### aliya

ok thanx but " can you please tell if there exists any X such that A.B=X(e^A.e^B)?"

8. Aug 10, 2010

### HallsofIvy

?? Of course their is:
$$X= ABe^{-(A+ B)}$$

9. Aug 10, 2010

### trambolin

I think he is trying to come up with a logarithm function. But that would be quite restrictive since the function wouldn't be distributive in general.