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#1 2013-07-15 03:09:05

mowgli
Member
Registered: 2013-07-15
Posts: 3

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!


Getting bamboozled by Maths since 1987 sad

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#2 2013-07-15 03:12:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 97,269

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.

If it ain't broke, fix it until it is.

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#3 2013-07-15 04:07:43

mowgli
Member
Registered: 2013-07-15
Posts: 3

Re: Matrix Exponent of Upper Triangular Matrix

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


Getting bamboozled by Maths since 1987 sad

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#4 2013-07-15 04:12:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 97,269

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.

If it ain't broke, fix it until it is.

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#5 2013-07-15 05:05:24

mowgli
Member
Registered: 2013-07-15
Posts: 3

Re: Matrix Exponent of Upper Triangular Matrix

Thanks a lot, you are the best.

big_smile:D:D:D:D:D:D:D:D:D


Getting bamboozled by Maths since 1987 sad

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#6 2013-07-15 14:41:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 97,269

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.

If it ain't broke, fix it until it is.

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