I need to compute e^A for the matrix

A= 0 ∏

....-∏ 0

where the diagonal are zeros and the other diagonal has pi on top and negative pi on the bottom.

I'm not quite sure where to start.

Thanks

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- Nov 26th 2008, 04:37 PMvictor1487Computing e^A
I need to compute e^A for the matrix

A= 0 ∏

....-∏ 0

where the diagonal are zeros and the other diagonal has pi on top and negative pi on the bottom.

I'm not quite sure where to start.

Thanks - Nov 26th 2008, 04:54 PMvincisonfire
is defined as

You can find that

if

then

If your prof wants you to evaluate those series then I don't know (I used Maple). Well I don't have the time... or both. - Nov 26th 2008, 06:00 PMchiph588@
should be

- Nov 26th 2008, 06:06 PMvincisonfire
I don't think so because it is

because the first term is 0 not 1 we must integrate from 1 to infinity not 0 to infinity. But I may be mistaking.

Here are the 10 first terms

-4.934802202

-0.876090073

-2.211352843

-1.976022212

-2.001829103

-1.999899529

-2.000004167

-1.999999864

-2.000000003

-1.999999999 - Nov 26th 2008, 10:06 PMchiph588@
well I typed e^A in my ti-89 and it gave me back where I is the identity matrix

- Nov 27th 2008, 04:26 AMvincisonfire
Yes you're right because we have to add the identity matrix at the beginning. SOrry.

then

Somebody knows how to calculate these sum by hand? - Nov 27th 2008, 07:49 AMawkward
You might consider starting by diagonalizing A--

Notice that

where

(I'm assuming you know how to go about diagonalizing a matrix; if not, there is an article on Wikipedia:

Diagonalizable matrix - Wikipedia, the free encyclopedia.)