Re: Matrix Exponential
- To: mathgroup at smc.vnet.net
- Subject: [mg34136] Re: [mg34101] Matrix Exponential
- From: BobHanlon at aol.com
- Date: Sun, 5 May 2002 04:48:44 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 5/4/02 7:21:09 AM, k.chourdakis at qmul.ac.uk writes:
>I am computing a few complex matrix exponentials for some Fourier
>transforms, and I keep getting the same kind of result that I cannot
>understand. As an example:
>
>=============================
>A) I can get the eigenvalues of the matrix.....
>IN:
>{{-1.850-1.993 \[ImaginaryI], -0.438-0.741
>\[ImaginaryI]},{-0.00919+0.01696 \[ImaginaryI],-10.80+0.938
>\[ImaginaryI]}} // Eigenvalues
>OUT:
>{-10.8017 + 0.937514 \[ImaginaryI], -1.84831 - 1.99251 \[ImaginaryI]}
>=============================
>B) I can also get the eigenvectors of the matrix......... and they are
>apparently distinct.
>IN:
>{{-1.850-1.993 \[ImaginaryI], -0.438-0.741
>\[ImaginaryI]},{-0.00919+0.01696 \[ImaginaryI],-10.80+0.938
>\[ImaginaryI]}} // Eigenvectors
>OUT:
>{{0.0196355 + 0.0888622 \[ImaginaryI], 0.99585+ 0.\[ImaginaryI]},
>{0.999998+0.\[ImaginaryI], -0.00148745 + 0.00140766 \[ImaginaryI]}}
>=============================
>C) But not the exponential, although they are related.
>IN:
>{{-1.850-1.993 \[ImaginaryI], -0.438-0.741
>\[ImaginaryI]},{-0.00919+0.01696 \[ImaginaryI],-10.80+0.938
>\[ImaginaryI]}} // MatrixExp
>OUT:
>Dot::"inf": "Input matrix contains an infinite entry."
>Dot::"inf": "Input matrix contains an infinite entry."
>\[Infinity]::"indet": "Indeterminate expression (0.+0.\[ImaginaryI])
>ComplexInfinity encountered."
>Dot::"mindet": "Input matrix contains an indeterminate entry."
>Inverse::"inf": "Input matrix contains an infinite entry."
>{{Indeterminate, Indeterminate},{0.00477109+
>0.00196731\[ImaginaryI],0.000017144-0.0000126169\[ImaginaryI]}}.Inverse[{{Com
plexInfinity,
>0}, {0, 1}}]
>=============================
>
>I am not sure which one of the many dubious ways Mathematica uses for
>its MatrixExp calculations.
>Could someone enlighten me? I have observed that it happens as the
>element differences become larger, although in the above example I would
>not say they are that large. Is it that matrices need some rebalancing
>before they are inserted in the MatrixExp[] function?
>
Works on my system
$Version
4.1 for Mac OS X (November 5, 2001)
MatrixExp[{{-1.85-1.993*I,-0.438-0.741*I},{-0.00919+0.01696*I,-10.8+0.938*I}}]
{{-0.0644759147679072 - 0.14367543421564122*I,
-0.01155045082979407 + 0.008587631193838957*I},
{0.0002981929070412231 + 0.00012295669549575546*I,
0.000017144031599151 - 0.000012616871918171252*I}}
Bob Hanlon
Chantilly, VA USA