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#1 2013-07-16 01:09:05

mowgli
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Matrix Exponent of Upper Triangular Matrix

Hi there everyone.

I was wondering if you can help me with the following question:

If I have a general upper triangular matrix such as:

A^n = -----d^n---n(u)d^n-1--------------(ignore dashes)
--------------0-------d^n

How to i find e^a and/or e^x using taylor series?

If the general matrix is difficult to compute onto text, consider any basic upper triangular matrix as an example.

Such as:

A = [2  4]
-----[0  2]

I'd be grateful for any help!

#2 2013-07-16 01:12:54

bobbym
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Re: Matrix Exponent of Upper Triangular Matrix

Hi;

Why wouldn't you just plug into the Taylor series?

What is a?

Start by computing A^n.














In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2013-07-16 02:07:43

mowgli
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Re: Matrix Exponent of Upper Triangular Matrix

How do you go from the final matrix shown to a matrix of exponential functions?

#4 2013-07-16 02:12:03

bobbym
Administrator

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Re: Matrix Exponent of Upper Triangular Matrix

Check post #2, that is the whole process.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2013-07-16 03:05:24

mowgli
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Re: Matrix Exponent of Upper Triangular Matrix

Thanks a lot, you are the best.

big_smilebig_smilebig_smilebig_smilebig_smilebig_smilebig_smilebig_smilebig_smilebig_smile

#6 2013-07-16 12:41:10

bobbym
Administrator

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Re: Matrix Exponent of Upper Triangular Matrix

Hi;

Not really, I had reconstruct it entirely from my notes. I did not even remember how before that.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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